Estimating the True Extent of Air Traffic Delays
by
YASMINE EL ALJ
B.Eng. in Civil Engineering (2000)
McGill University, Montreal, Canada
Submitted to the Department of Civil and Environmental Engineering
in Partial Fulfillment of the Requirements for the Degrees of
Master of Science in Transportation
and
Master of Science in Operations Research
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2003
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
©2003 Massachusetts Institute of Technology.
JUN 0 2 2003
All rights reserved.
UIBRARILES
Signature of Author:
Depart66ent of Civil and Envi4 onmental Engineering
January 21, 2003
A
Certified by:
Amedeo R. Odoni
T. Wilson Professor of Aeronautics and Astronautics
and Civil and Environmental Engineering
Thesis Supervisor
riI~
Accepted by:
I
John N. Tsitsiklis
Professor of Electrical Engineering and Computer Science
Co-Director, Operations Research Center
Accepted by:_____________________________
Oral Buyukozturk
Chairman, Departmental Committee on Graduate Studies
Estimating the True Extent of Air Traffic Delays
by
Yasmine El Alj
Submitted to the Department of Civil and Environmental Engineering on January 21,
2003 in partial fulfillment of the requirements for the degrees of Master of Science in
Transportation and Master of Science in Operations Research.
ABSTRACT
Most air traffic delay measures assess delays relative to schedule. Over the past decades,
however, airline schedules have been adjusted to take into account airspace congestion
and yield better on-time performance. In that context, delay measures that are using
scheduled times as a benchmark are of very limited use in assessing airport and airspace
system congestion, since delay has already been built into the schedule.
The primary goal of this thesis is to develop a measure that will estimate "true" delays
that are not sensitive to schedule adjustments. In order to calculate "true" delays, we
compute the difference between the actual gate-to-gate time and a theoretical benchmark,
the "baseline". The baseline time to be used is O-D specific and is defined here as the
gate-to-gate time from origin to destination under optimal (non-congested) conditions.
We choose the fifteenth percentile of reported statistics on gate-to-gate time as an
estimator of the baseline. We then compute baseline times for 618 major O-D pairs.
Using the baseline times, we compute "true delays" on these 618 O-D pairs and observe
that they are about 40% to 60% larger than delays relative to schedule.
We also develop two methods to attribute O-D delays to the origin and destination
airports. Using these methods, we determine that airports incurred about 5 to 13 minutes
of delay per operation in 2000, depending on the airport under consideration. Airport
rankings according to "true" delays are compared to airport rankings obtained from
OPSNET delay statistics. The comparison suggests that, although OPSNET statistics
underestimate the magnitude of delays, they yield very comparable airport rankings and
can therefore be used to rank airports with respect to congestion.
Finally, we change perspective and look at the development of probabilistic models for
designing flight schedules that minimize delays relative to schedule. We use the simple
case of an airline scheduling an aircraft for a round trip to illustrate the complexities and
uncertainties associated with optimal scheduling.
Thesis Supervisor:
Amedeo R. Odoni
T. Wilson Professor of Aeronautics and Astronautics and Civil and
Environmental Engineering
4
ACKNOWLEDGEMENTS
I am grateful for the generous support of the National Center of Excellence for Aviation
Operations Research (NEXTOR), which funded this thesis work.
I would like to thank my research advisor, Professor Amedeo Odoni, for his
encouragement, wisdom, and patience. I deeply appreciated his academic guidance,
which greatly enhanced my educational experience at MIT.
I would like to thank all those people in CTL and ICAT that have made my experience at
MIT more enriching, enjoyable, and educational. Special thanks to my lab mates in 35220, for their thoughtfulness and humor. I will remember the laughs, lunches, and coffee
breaks spent discussing life's issues.
I am also very grateful for the untiring support of Pavlo Pshyk, both before and
throughout my stay at MIT. His loving and caring helped me get through this challenging
time. Thanks for believing in me!
I would finally like to thank my family, Jihane, Maman, and Papa for their understanding
and for their motivation in the final phases of my thesis. I especially would like to thank
my mother for her unwavering encouragement, positive thinking, and stress-relief
techniques.
5
6
TABLE OF CONTENTS
List of Figiures
9
List of Tables
11
Chapter 1. Background and Motivation
13
1.1 The economic and operational impacts of delays.................................13
1.2 Current estimation of delays.........................................................16
1.3 Objectives of the thesis...............................................................
17
1.4 Literature review .........................................................................
18
1.5 T hesis outline............................................................................23
27
Chapter 2. Anatomy of Flight Time
27
2.1 T erm inology ...........................................................................
2.2 Factors affecting gate-to-gate time...............................................30
2 .3 D ata ...............................................................................
. . ..34
2.4 Potential delay measures.........................................................
Chapter 3. Baseline Estimation
42
49
3.1 Baseline time estimation methodology.............................................49
3.2 Application: evolution of O-D delays from 1995 to 2000....................55
Chapter 4. Role of Airports in Generating Delays
63
4.1 Estimation of airport delays.........................................................63
4.2 Analysis and interpretation of results..............................................81
Chapter 5. Applications
89
5.1 Logan airport annual delays.........................................................89
5.2 Airport rankings....................................................................92
7
Chapter 6. Optimal Scheduling: A simple case study
101
6 .1 C on text.................................................................................10
2
6.2 Objective functions...................................................................106
6 .3 R esu lts..................................................................................I
II
6 .4 C onclu sion s............................................................................12
1
Chapter 7. Conclusion
123
7 .1 Summ ary ..............................................................................
12 3
7.2 Future research directions...........................................................126
References
129
Appendices
131
Appendix
................................................................
131
Appendix B: Detailed results...........................................................133
Appendix C: Airport delay attribution.................................................137
Appendix D: Standard deviations......................................................143
8
LIST OF FIGURES
Figure 1.1: Evolution of revenue passenger (ton-miles) from 1981 to 2000..............14
Figure 2.1: Flight time decomposition............................................................28
Figure 2.2: Variation and evolution of scheduled vs. actual gate-to-gate times for three
origin-destination pairs.............................................................................35
Figure 2.3: Evolution of average airborne, taxi in, and taxi out times from 1995 to
2 0 00 .............................................................................................
. . .. 36
Figure 2.4: Annual evolution of gate-to-gate percentiles...................................37
Figure 2.5: D irectionality ........................................................................
38
Figure 2.6: Influence of seasonality on gate-to-gate times.................................38
Figure 2.7: Influence of day of the week on gate-to-gate times..............................39
Figure 2.8: Influence of time of day on gate-to-gate times.................................40
Figure 2.9: Comparison of maximum, minimum, average, and 15 h percentile gate-to-gate
.. ... 41
......
tim es...........................................................................
Figure 2.10: Aircraft fleet evolution...........................................................42
Figure 3.1: Sensitivity of the BOS weighted baseline to the percentile chosen............52
Figure 3.2: Baseline times per O-D pair..........................................................53
Figure 3.3: Average "true" delays per O-D pair in 2000 (min/op) ........................ 54
Figure 3.4: Evolution of the weighted average "true" delay from 1995 to 2000......56
Figure 3.5: Distribution of the delay increase between 1995 and 2000....................57
Figure 3.6: Comparison of overall average true delay versus other delay measures.......59
Figure 3.7: Sensitivity of on-time performance statistics to the delay definition used .... 60
Figure 4.1: Step A2 - Description of the iterative process.................................68
Figure 4.2: Comparison of Step Al and Step A2 results for 2000 ........................ 70
Figure 4.3: Sensitivity of aggregate overall delay results to fraction p chosen.............80
Figure 4.4: Airport delays in 2000 calculated as a function of the methodology...........82
Figure 4.5: Standard deviation of taxi out delays grouped by origin airport vs. destination
. . 85
airp ort............................................................................................
9
Figure 4.6: Standard deviation of taxi in delays grouped by origin airport vs. destination
airp ort.................................................................................................8
6
Figure 4.7: Standard deviation of airborne delays grouped by origin airport vs. destination
a irp o rt.................................................................................................8
7
Figure 5.1: Correlation of airport rankings using different criteria (Spearman rank
correlation test)...................................................................................
98
Figure 6.1: Spatial and temporal description of flight path..................................102
Figure 6.2: Probability distribution functions of actual transit times between A and B.. 102
Figure 6.3: Probability distribution of arrival delay at B.....................................103
Figure 6.4: Probability distribution of departure delay at B..................................104
Figure 6.5: Probability distribution of elapsed time between scheduled departure at B
(td)
and arrival at A (Cases 1 &2)..............................................................105
Figure 6.6: Probability distribution of arrival delay at A (Case 0)..........................105
Figure 6.7: Probability distribution of arrival delay at A (Case 1)..........................105
Figure 6.8: Probability distribution of arrival delay at A (Case 2)..........................106
Figure 6.9: Optimal solutions for case 0, 6=0..................................................116
Figure 6.10: Optimal solutions for case 0, 6=1................................................117
Figure 6.11: Optimal solutions for case 1, 6=0................................................118
Figure 6.12: Optimal solutions for case 2, 6=0................................................118
Figure 6.13: Optimal solutions for case 2, 6=1................................................119
10
LIST OF TABLES
Table 1.1: Typical delay cost breakdown for an airline......................................15
Table 4.1: Average airport delays (min/op) obtained using Step Al.........................65
Table 4.2: Average airport delays (min/op) obtained using Step A2.....................69
Table 4.3: Average airport delays (min/op) obtained using Step BI.........................73
Table 4.4: Average airport delays (min/op) obtained using Step B2......................75
Table 4.5: Comparison at the aggregate level of airport delays obtained using Step A2
an d S tep B2 ..........................................................................................
76
Table 4.6: Average airport delays (min/op) obtained using Step B3......................78
Table 4.7: Average airport delays (min/op) obtained using Step B4......................81
Table 4.8: Comparison at the aggregate level of airport delays obtained using Step A2
an d S tep B4 ..........................................................................................
82
Table 4.9: Comparison of spreads for Step A2 and Step B4...............................83
Table 5.1: BO S airport delays ..................................................................
90
Table 5.2: Total number of operations at BOS airport ........................................
90
Table 5.3 Total annual delay at Logan airport.................................................91
Table 5.4: Airport rankings by proportion of flights delayed (OPSNET) .................. 94
Table 5.5: Comparison of airport rankings using Step A2, B4, and OPSNET delays......94
Table 5.6: Correlation between airport rankings.............................................95
Table 5.7: Airport delay rankings using different criteria.....................................97
Table 6.1: Objective function terms for objective function 1................................108
Table 6.2: Objective function terms for objective function 2................................109
Table 6.3: Objective function terms for objective function 3................................110
Table 6.4: Solutions for objective function 1...................................................112
Table 6.5: Solutions for objective function 2...................................................113
Table 6.6: Solutions for objective function 3...................................................115
Table 6.7: Detailed case-by-case optimal solutions for objective function 4......
Table 6.8: Optimal solutions for OF 4 as a function of K, L, Ca, and C9....
......
.. 120
121
11
12
CHAPTER 1: BACKGROUND AND MOTIVATION
1.1- Background: The economic and operational impacts of delays
Air traffic increased dramatically from the 1980s to the year 2000: revenue passenger
ton-miles doubled from 1985 to 2000 and grew by about 25% from 1995 to 2000 (Figure
1.1). In this context, it is not surprising that the Air Traffic Control (ATC) system and
National Airspace System (NAS) were having trouble managing the increase in traffic
and congestion. This growth in air traffic has increased work loads for controllers,
strained capacity at certain airports and in some portions of the airspace, as well as
increased en-route holding and the number and frequency of ground delay programs.
13
Evolution of Revenue Passenger (ton-miles) from 1981 to
2001
00
8.E+07
-
7.E+07
-
----
6.E+07
rz5.E+07
4.E+07
3.E+07
0
2.E+07
1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
-u--All Services: Revenue Passenger ton-miles in thousands
Scheduled Service: Revenue Passenger ton-miles in thousands
--
Figure 1.1: Evolution of revenue passenger (ton-miles) from 1981 to 20011
Increased traffic levels have ultimately resulted in congestion and delays at airports and
in the airspace. The main goal of this thesis is to estimate the magnitude of these delays
and examine their evolution over time.
The resulting delays have had serious adverse impacts on both airlines and passengers. In
fact, prior to the events of September 11, 2001-, the poor on-time performance of airlines
2
and the high incidence of flight delays were the focus of much attention by the media
and the general public. Delays contribute greatly to a decrease in perceived levels of
service for passengers; the larger the delay, the lower the passenger's satisfaction. From
the airline's perspective, delays can result in major operational disruptions and significant
costs. Delays propagate quickly throughout the airline's network: when a flight is
delayed, the next flight using the aircraft is also likely to be delayed, if no slack has been
built into the schedule. Some of the negative impacts of delays include crew-scheduling
disruptions, flight cancellations, and re-booking of passengers that have missed their
connections. Table I provides a typical breakdown of delay costs to an airline. The
FAA's Office of Aviation Policy and Plans (APO) estimated that in 1994, the direct
Data obtained from the Bureau of Transportation Statistics website
According to Mayer and Sinai, the New York Times, Wall Street Journal, and USA Today alone
published 58 articles in 2000 with air traffic delay or airline delay in the title.
2
14
operating cost to airlines associated with flight delays in the US exceeded $2.5 billion
(based on an average aircraft operating cost of $1500 per hour).
Holding
48%
Yield Reduction (re-booking)
16%
Passenger Care
2%
Bound aircraft capacity
11%
Flight crew
5%
In-flight acceleration
4%
Station cost
3%
Processing cost
1%
Lost Yield
7%
Supplier Capacity
4%
Table 1.1: Typical delay cost breakdown for an airline (Adapted from
Source: Booz-Allen & Hamilton)
Since 1987, carriers have been provided with additional incentives to reduce delays
relative to schedule and improve their on-time performance, with the introduction of the
On-Time Disclosure Rule (OTDR) by the Department of Transportation (DOT). The
OTDR makes the on-time performance of US carriers available to the public. In OTDR, a
flight is considered on time if it arrives within 15 minutes of its scheduled arrival time.
The OTDR rule makes it even more important for airlines to be on time since an airline
that incurs substantial delays is likely to suffer from a negative public perception, and in
turn will become less attractive to passengers.
Because delays are disruptive and costly, airlines are very interested in improving their
on-time performance. An effective way they came up with to deal with this problem is to
adjust their scheduled flight times. In his thesis, Shumsky (1993)3 showed that over the
3 His work will be examined in more detail in the literature review section.
15
years, as actual transit times increased because of congestion and inefficiencies in the
airspace and in the airport system, carriers kept lengthening their schedules to improve
their on-time performance and avoid low ratings on delays.
1.2- Motivation
The delay measure used most commonly is that of the US Department of Transportation
(US DOT), which is: Delay = (Actual Arrival Time) - (Scheduled Arrival time). This
DOT-measured delay is a function of the scheduled arrival time, and is therefore sensitive
to changes in the flight schedule.
Schedule adjustments, however, prevent the US DOT delay measure from being effective
in estimating the true extent of air traffic delays, or in gauging the state of the airspace
and air traffic control systems. Real, congestion-related delays are not being accounted
for in this measure because over time they are absorbed in the schedule. Moreover,
because delays are measured against an ever-increasing benchmark (i.e. scheduled arrival
time), their comparison in time is not always meaningful. Since our goal is to estimate
delays due to increased demand levels (which result in congestion) and examine their
evolution, we need to develop an alternative metric that will not have the shortcomings of
the US DOT measure.
Note that despite the numerous and frequent schedule adjustments made by airlines, the
delay definition used by the US DOT continues to accurately measure delays relative to
schedule. It also remains a measure of importance to the passengers as it helps them
assess how reliable their trip times will be. Later in this thesis, we will show that delays
relative to schedule underestimate the true extent of delays.
16
1.3- Objectives of the thesis
This thesis focuses on deriving a methodology to estimate the true extent of air traffic
delays (including congestion-induced delays) and examining long-term trends over time.
We develop a new metric to estimate delays due to congestion in airspace and at airports,
as well as delays due to other system inefficiencies. Congestion typically exists because
of increased demand levels or insufficient capacity. Capacity, in turn, is affected by
weather conditions and ATC performance. By comparing the evolution of "true" delays
over time, one will be able to monitor the health of the National Airspace System (NAS)
and its ability to keep up with the increasing traffic levels.
The proposed alternative delay measure consists of comparing actual gate-to-gate time to
a consistent benchmark, the baseline. The idea is to create a baseline, which would
approximate the gate-to-gate congestion-free time. The baseline has to be consistent in
time, specific to each Origin-Destination pair considered, and independent of competition
and demand levels. Under this definition, delays due to late passengers and supporting
services will not be taken into account. Only inefficiencies due to congested airspace and
airport capacity constraints will be reflected in this new delay measure. This baseline will
allow us to calculate true delays on the different O-D pairs, and to monitor their evolution
over time.
Another objective of this thesis is the development of methodologies to evaluate relative
congestion at each airport. Procedures to attribute "true" O-D delays to airports allow us
to pinpoint specific sources responsible for the true delays. Identifying the bottlenecks in
the system can help focus efforts towards congestion relief. Lastly, the final chapter
demonstrates how complex it is for an airline to schedule its flights so as to minimize
delays relative to schedule.
Several applications are illustrated throughout the thesis. All computations are based on a
sample of flights operating on 618 O-D pairs, between 27 U.S. airports. However, the
methodologies described can be applied to the US network as a whole.
17
1.4- Literature review
Three papers are summarized in this section:
-
the first two papers discuss air traffic delays and appropriate ways to measure
delay. Both of these papers show that airlines are indeed lengthening their
schedules. They discuss the need for a consistent baseline against which to
estimate delays, in order to allow for a consistent monitoring of the performance
of the national airspace system and for tracking the evolution of delays. The
development of a methodology that has these desirable properties is also the main
goal of this thesis.
-
the third paper examines the variability in airborne time on a given O-D pair and
the attribution of the variability to one of four sources. In this thesis, we will look
at the different factors causing variability in gate-to-gate time and we will try to
estimate the impact of airport and airspace congestion on gate-to-gate time.
A summary of each paper and its relation to this thesis follows.
1.4.1 Shumsky: "The response of US Air Carriers to the DOT on-time disclosure
rule"
In his Master's thesis, Shumsky (1993) examined strategies used by different airlines for
producing an optimal schedule with respect to on-time performance, gauged the success
of their efforts and evaluated the effectiveness of the OTDR rule. He also proposed some
approaches to optimal scheduling.
Upon examination of a 1985-1991 flight sample, Shumsky showed that carriers' reactions
to the OTDR differed in the size and timing of their schedule changes. Carriers also used
different methods to determine how to distribute those changes among flights. Analysis
18
showed that some airlines used a simple linear relationship between on-time performance
of a flight in one year and the number of minutes added to that flight's schedule the next
year. Others used a more sophisticated 'marginal gain approach': they seemed to
lengthen the scheduled gate-to-gate times of those flights that were most likely to benefit
from such lengthening and to decrease the scheduled gate-to-gate times of those that were
least likely to suffer from the change.
Shumsky continued by examining the effectiveness of the carriers' scheduling decisions
and explored whether past performance could be used to design a schedule that optimized
on-time performance. He proposed two strategies for generating a schedule, given a fixed
"budget" of extra minutes. The first strategy ignores previous performance and distributes
the budget uniformly among all flights (uniform strategy); the second is an optimization
procedure (MIP) using on-time performance as the sole objective. The 1991 schedules of
American, United, and Delta Airlines were then generated under the two strategies. An
examination of expected on-time performance of the flights under both these schedules
was then performed. Results showed that the uniform strategy performed as well as both
the MIP and the carriers' own schedules.
Shumsky's observations provide the motivation for this thesis. Shumsky showed that as
actual flight times got longer, airlines increased their scheduled flight times in order to
maintain good on-time performance: if the carriers had not lengthened their schedules
from 1987 to 1991, the percentage of flights arriving on-time would have been as much
as 20% lower than reported in 1991. He also pointed out that "on-time statistics published
in the ATCR are not a reliable indicator of the state of the air traffic system. As actual
transit times rise, carriers lengthen their scheduled transit times as well, so that increasing
congestion or inefficiency are reflected in the carrier's schedules but not in the on-time
statistics." This thesis builds on these observations and attempts to provide an alternative
metric that will not depend on the schedule and will accurately measure "true" delays.
19
1.4.2- Mayer and Sinai: "Hubbing versus the 'Trauedy of the Commons': Why does
Every Flight by US Airways from Philadelphia Seem to be Late?"
Mayer and Sinai (2001) explored two hypotheses to explain the extent of air traffic
delays: the first is the absence of pricing of the externalities that adding a flight imposes
on other users ("the tragedy of the commons") and the second is hubbing.
They showed that a high portion of delays is due to hubbing activity. They also found
that hubbing and market concentration have opposing effects on delays: hubbing activity
tends to increase delays while market concentration tends to lead to a reduction in delays.
The hubbing effect empirically dominates. In their paper, Mayer and Sinai showed that:
- At hubs, airlines partially offset previously documented increases in travel time through
padded schedules, but flights to or from a hub still have above average delays and a
greater probability of being delayed at least 15 minutes.
- Travel time has increased significantly over the last 13 years and congestion has
increased no matter which measure of delay is used.
- The average delay4 increased by nearly two-thirds between 1988 and 2000 and more
than doubled from the best year (1991) to the worst (2000).
- airlines do not appear to account completely for actual gate-to-gate time in setting their
schedules. Average actual gate-to-gate time always exceeds scheduled gate-to-gate time
in all years. Scheduled travel times, in their findings, seem to increase by only two-thirds
of the amount of the increase in actual times.
Due to the fact that on-time performance can be artificially improved by increasing
scheduled times for flights, Mayer and Sinai developed an alternative benchmark to
measure delays. They used minimum travel time5 to look at overall change in travel time:
they estimated that the average flight, in 2000, arrived 32 minutes later than it would
have if it left on time and required the minimum feasible travel time for the route.
4 Delay defined as actual arrival time minus scheduled arrival time
5 Defined as the shortest observed travel time on a given route in a particular month
20
They also found that over the time period 1989-2000, the minimum travel time has
increased from 89 to 94 minutes. They concluded that increases in the total flight load
have slowed the performance of the entire air traffic control system. Thus, of the
additional nine minutes of travel time on the average route since 1988, approximately 5.2
minutes is due to overall increases in minimum travel time and the remaining 4 minutes
is accounted for by increases in average travel time above the minimum travel time.
Mayer and Sinai also advocate the need for an alternative benchmark to accurately
measure delays. In their paper, they used the minimum travel time recorded over a month
as the benchmark for the delay-free travel time on any given route. In this thesis, we will
discuss some of the problems associated with using the minimum travel time and why we
choose to use a different benchmark.
1.4.3- Thomas Willemain: "Estimatin2 the Components of Variation in Flight
Times"
In his paper, Thomas R. Willemain estimated the systemic component of airborne time
variability (caused by weather or by en-route terminal area congestion) from day to day
and flight to flight. He also attributed the variability to one of four sources: the regional
airspace as a whole (day effect), the airspace at the departure airport (origin effect), the
airspace at the arrival airport (destination effect), or the en route airspace (en-route
effect).
Willemain outlined two variants of this methodology: one using deviations from long-run
average airborne times, and the other using deviations from estimated en route times filed
in flight plans. His methodology is based on the assumption that:
Deviation =Day effect + Origin Effect + Destination Effect + En-Route effect
He used a non-linear program that minimizes the sum of absolute values of the residuals
(en-route effect) from the fitted additive model to estimate the different effects. The
analysis can be repeated for every day of the sample period and the distribution of the
21
estimated effects can then be computed. Unusually high values of an estimate point to a
specific source of airborne delays. A large value for the day effect indicates problems
throughout the region containing the O-D pairs. Large values associated with origin
effects or destination effects indicate a problem with the origin/arrival airport. A large
residual suggests delays in the airspace between a particular O-D pair.
This methodology was applied to a sample of flights operating in the Eastern US in the
afternoon during the January-March 2001 period. After computing the distribution of
estimated day, destination, and origin effect over the period, Willemain observed that:
-
there was a strong negative correlation between origin and destination effects at
the same airports;
-
correlations between en-route pairs ranged from zero to very strong depending on
the O-D pairs under consideration. The relative direction of two flights had a large
influence on the correlation of their estimated daily en-route effects, which
suggested that en-route effects were in fact measuring the impact of winds aloft.
He then decided to analyze deviations from estimated times en-route, in order to exclude
the impact of winds aloft and to reduce the effect of nuisance variation caused by the
differences in aircraft weights or flight paths. He used a sample of flights from FebruaryApril 2001 to estimate the different effects. He found that:
-
the estimated origin effects were less variable than the estimated destination
effects, and were also more tightly clustered around zero. Destination effects were
more pronounced than origin effects;
-
the estimated en-route effects were quite pronounced relative to origin and
destination effects;
-
the correlation between origin and destination effects was very weak: the inverse
relationship discovered using deviations from average airborne times on his first
sample no longer held;
-
the correlations of en-route effects were weaker.
22
Willemain examined the systemic variability of airborne times and developed a
methodology to attribute it to one of four sources. In this thesis, we will use a similar
reasoning and attribute O-D delays to the airport of origin, the airport of destination, and
the airspace. In contrast to his approach, we are not interested in analyzing the causes of
daily fluctuations; we are only concerned with long-term variability and trends in gate-togate times.
1.5- Thesis Outline
The principal goals of this thesis are:
0
To define consistent baseline times for flights operating between 27 of the busiest
airports in the United States (which represent about 600 major Origin-Destination pairs).
59% of total passenger enplanements in the US take place at the 27 selected airports.
*
To estimate the true extent of air traffic delays and compare their evolution from 1995
to 2000.
*
To define a suitable methodology for attributing O-D delays to airports and to
examine the correlation between average delay on a specific O-D and its airports of
origin and destination.
0
To compare delay results based on the methodologies developed in this thesis to
results based on commonly used delay measures.
0
To develop a model that illustrates the complexities associated with designing airline
schedules with the goal of minimizing delays relative to schedule.
Chapter 2 focuses on terminology and delay measures, including a case study of three
specific O-D pairs illustrating the type of information that can be extracted from the data.
Properties of the "delay relative to schedule" measure are compared with a measure that
would involve taking the difference between actual gate-to-gate time and a baseline.
Factors affecting gate-to-gate time variability (seasonality, day of the week, time of day,
weather/winds, runway configurations and gate assignments, flight path, aircraft type,
direction of travel, congestion of en-route space, congestion of airports and terminal
23
airspace around them) and their potential impact on the baseline derivation are discussed.
Lastly, the properties of potential baseline estimators are discussed and compared. After
examining many estimates, we decide that for our purposes it would be most appropriate
to use a percentile of gate-to-gate time in the 5-20% range.
Chapter 3 outlines the procedure used to define consistent O-D-specific baseline times.
Baseline times for each of the 618 O-D pairs under consideration are computed using the
fifteenth percentile of gate-to-gate time, averaged over a four-month period. "True" O-D
delays are then computed by taking the difference between actual gate-to-gate time and
the baseline. Their evolution from 1995 to 2000 is analyzed. We find that the average
"true" delay on the 618 O-D pairs has increased from 11.1 minutes per flight in 1995 to
16.9 minutes in 2000 (52% increase). On 75 of the 618 O-D pairs considered, true delays
more than doubled over the 1995-2000 period. When "true" delays are compared to
delays relative to schedule, we find that "true" delays were about 40% to 60% greater
than delays relative to schedule. Analysis of "delays relative to scheduled transit time"
and "delays relative to schedule" also suggests that although airlines seem to be able to
accurately predict gate-to-gate times, they are not good at predicting departure times,
which is the reason why delays relative to schedule are incurred.
Chapter 4 details two methodologies to be used to attribute O-D delays to airports, as
airports are usually the bottlenecks in the air transportation system. The first method is an
iterative method based on the attribution of a variable portion of the overall O-D delay to
the airports of origin and destination, depending on the relative congestion at those
airports. The second method is based on the decomposition of gate-to-gate time into its
three components (taxi out time, airborne time, taxi in time), the calculation of individual
component delays, and the attribution of component delays to the relevant airport. Results
obtained using both methods show that airport delays increased over the 1995-2000
period: the average increase in delays at the 27 airports considered was of the order of 2
to 3 minutes per operation, which represents an increase of 40% to 53% depending on the
method used. Further analysis on individual component delays suggests that there is a
24
strong correlation between taxi out delay and airport of origin, as well as between taxi in
delay and destination airport.
Chapter 5 focuses on two applications of the methodologies outlined in Chapters 3 and 4.
The first application consists of the estimation of total annual delays at Logan airport
(BOS) using average delay figures obtained from Chapter 4. Our best estimates showed
that annual "true" delays at Logan were on the order of 80,000 to 105,000 hours for the
year 2000. The second application consists of deriving delay-rankings of airports based
on the individual airport delays obtained from Chapter 4, and comparing them with the
FAA's and DOT's airport rankings (such as OPSNET delays, ASPM delays, etc) using
the Spearman correlation test. We find that, although OPSNET statistics severely
underestimate delays, they yield very similar rankings to those obtained using the
methods we derived in Chapter 4.
In Chapter 6, we change our perspective and show why it may be very difficult for
airlines to optimize their schedules so as to achieve high schedule compliance records.
We use a simple case (an aircraft scheduled for a round trip, uniform probability density
functions for actual transit times) to point out some of the complexities and
interdependences in the schedule that make airline scheduling so complex. We also
examine the impact of the choice of the objective function on the optimal scheduling
solution obtained. In our example, scheduling strategies depend on the relative perceived
costs of reduced aircraft utilization, on the one hand, and of delays, on the other. Results
obtained in our example show the importance of ensuring that the schedule minimizes the
delay on the first leg of the trip, so as to avoid the propagation of delays on the remaining
legs of an aircraft's itinerary.
Finally, Chapter 7 provides a summary of the findings of this thesis and suggests
potential areas for future research.
25
26
CHAPTER 2: ANATOMY OF FLIGHT TIME
The principal objective of this thesis is to determine a set of baseline times that can be
used now and in the future to estimate "true" delays for flights between 27 of the busiest
airports in the United States. The goal of Chapter 2 is to discuss appropriate estimates for
these baselines, upon examination of the factors affecting the variability of gate-to-gate
times. Section 2.1 introduces terminology. Section 2.2 takes a closer look at some of the
factors affecting gate-to-gate times. Section 2.3 describes the data used and illustrates the
type of information that can be extracted from the data. Section 2.4 discusses in more
detail the purpose of the baselines and proposes estimates to approximate them.
2.1- Terminology
A flight can be decomposed into three time segments:
1.
Taxi-out time
2. Airborne time
3. Taxi-in time.
27
Taxi-out
Push-in
Wheels-on
W
Wheels-off
Pushback
Airborne
T
Taxi-in
Ariiyal.
epaiTe-
*A
Gate-to-gate time
Figure 2.1: Flight time decomposition
In this connection, the following time instants and intervals can be defined (Figure 2.1):
. Push-out Time: The time at which the aircraft leaves its departure gate. This time
corresponds to the moment at which the doors are closed and the brake is released. At
that time, a switch is activated and the time is recorded.
.
Wheels-Off Time: The time at which the wheels leave the ground (take-off time).
A switch that is activated when the wheels leave the ground records this time.
.
Wheels-On Time: The time at which the wheels make contact with the ground
(landing time). A switch that is activated when the wheels touch the ground records
this time.
Push-in Time: The time at which the aircraft reaches its arrival gate. It is taken as
.
the time at which the brake is secured.
.
Taxi-out: This is the time between pushback and wheels-off.
Taxi-out time= (Wheels-off time) - (Push-outtime)
.
Airborne time: This is the time between wheels-on and wheels-off.
Airborne tine= (Wheels-on time)- (Wheels-off time)
.
Taxi-in: This is the time between wheels-on and push-in.
Taxi-in time= (Push-intime)- (Wheels-on time)
28
*
Actual Gate-to-Gate time or Actual Block Time: This represents the actual transit
time and is defined as the time interval between pushback and push-in.
Actual Gate-to-Gatetime= (Push-in time) - (Push-out time)
.
Scheduled gate-to-gate time: this represents the total scheduled block time, from
scheduled departure time to scheduled arrival time.
Scheduled gate-to-gate time=(Scheduled arrivaltime) - (Scheduleddeparturetime)
2.1.1
Delay relative to schedule vs. true delay
There is a fundamental difference between true delay and delay relative to schedule. The
US DOT measure of delay, (Actual arrivaltime)- (Scheduled arrival time), is a measure
of delay relative to schedule. The benchmark against which the delay is measured is
represented by the scheduled arrival time of each flight, which in turn depends on the
scheduled gate-to-gate time. As discussed in the previous chapter, this measure is
sensitive to propagation of delays in the network as well as to adjustments to the
scheduled duration of flights, and does not allow for a meaningful comparison of delays
over time.
On the contrary, in the case of true delay, the benchmark should be a "baseline" which
represents a standard estimated gate-to-gate time for completing a particular flight under
congestion-free conditions. Thus, True Delay= (Actualgate-to-gate time) - (Baseline).
The baseline, which will be defined in more detail in Chapter 3, should be characteristic
of each origin-destination pair for any given type of aircraft. The baseline should also be
independent of demand levels.
29
2.2 Factors affecting gate-to-gate time
As indicated, true delay is measured as the difference between actual gate-to-gate time
and a benchmark. It is therefore useful to first take a closer look at some of the factors
that contribute to gate-to-gate variability on a given origin-destination pair. It will be
important to keep all those factors in mind when deciding which baseline to choose, in
order to ensure consistency over time.
The following are potential factors contributing to the variability in gate-to-gate times on
a given O-D pair.
2.2.1
Seasonality
Seasonality may impact gate-to-gate time for at least two reasons.
First, scheduled
operations (frequency, departure times) vary with the season. For example, summer and
fall are typically the busiest seasons for air travel. With more flights scheduled during
these seasons, the airspace and airports become more congested and gate-to-gate times
may increase. Second, seasonality may be strongly linked to weather. Bad weather
usually results in major delays; flights operating during the winter may therefore incur
greater gate-to-gate times.
2.2.2
Day of Week
Day of the week may influence gate-to-gate time. Some days of the week are busier than
others. Friday is typically the busiest day for air travel in the United States, as business
travelers return home for the weekend and leisure travelers fly to their chosen destination.
In contrast, Saturday is the least busy day for air travel in most areas. This might translate
30
into shorter gate-to-gate times for flights operating on Saturdays and longer gate-to-gate
times for those operating on Fridays.
2.2.3
Time-of-day
Time-of-day may influence gate-to-gate time because the number of scheduled operations
may vary with the time of the day. For example, very few operations are usually
scheduled at off-peak hours (between 10 PM and 6AM) because they are not convenient
for passengers. Because of the relatively small number of aircraft operating during these
hours, there is very little congestion, which may result in shorter than average gate-togate times.
2.2.4
Weather/ Winds
Winds may have a strong influence on airborne time, especially for longer-haul flights.
Favorable winds can significantly decrease airborne time while unfavorable winds can
result in longer airborne times and higher fuel consumption.
Weather can affect both airspace conditions and airport conditions. A particularly bad
weather pattern along the preferred flight path can result in a flight modifying its route,
resulting in a longer gate-to-gate time. Bad weather at an airport is likely to result in
increased holding time in the airspace.
Bad weather also results in reduced airport capacity by causing increases in minimum
separations and longer queues for take-off and landing. It may also result in ground
holding, increased taxi out and taxi in times, and, in turn, increased gate-to-gate times.
2.2.5
Runway and Gate Assignments
The runway configuration in use at an airport may affect the three components of gate-togate time: taxi out, airborne and taxi in. Taxi out/in times are affected by the location of
31
the departure/arrival gate with respect to the location of the departure/arrival runway.
Airborne time can also be affected by the runway assignment: taking off from any given
runway configuration leads to a specific ascent path, which might be very different from
the path associated with another departure runway, therefore potentially increasing or
decreasing flight distance.
2.2.6
Route/ Flight Path
The flight path may affect airborne time. Flight paths depend on weather conditions,
runway configurations in use, and demand levels (see "airspace congestion" below).
They may also depend on the airline and the pilot.
2.2.7
Aircraft Type
Aircraft type may influence airborne time, because of the different speeds and altitudes at
which different aircraft fly. Aircraft size may also affect queuing time, if air traffic
controllers attempt to sequence aircraft on landing or take-off in light of wake vortex
separation requirements.
2.2.8
Direction of Travel on any given O-D pair
Gate-to-gate times on a given O-D pair may depend strongly on the direction of travel,
due to prevailing direction of winds aloft (e.g., jet stream) and the orientation of the
runways at the airports of origin and destination.
2.2.9
Coniestion of en-route airspace
32
Airspace congestion affects airborne times and may result in aircraft flying at less than
optimal speed or on non-optimal flight paths or, on some occasions, being subjected to
airborne or ground holding. This is particularly true on short to medium hauls for aircraft
heading to popular airports. For example, aircraft heading from Chicago to New York
can be "queuing" (miles-in-trail) almost from their departure and until landing and are
therefore never able to reach their optimal speed. In Chapter 4, we shall estimate how
much of the O-D delay is actually attributable to en-route congestion.
2.2.10 Congestion of airports and terminal airspace around them
Increases in demand levels can lead to airport congestion, as more flights attempt to
depart or arrive at an airport. Bad weather usually compounds the situation because it
results in reduced airport capacity. In Chapter 5, the relationship between delays at a
given airport and reduced airport capacity will be illustrated.
Variability in gate-to-gate times attributable to the factors described above is due to the
fact that flights on a given O-D pair will not always operate under the same set of
periodic (season, time, day), meteorological (wind, weather), or physical conditions
(runway configuration and gate assignment, flight path, etc). In this thesis, we are only
concerned with variability due to airspace and airport congestion. However, the existence
of other factors complicates the task of estimating the exact impact of airspace and airport
congestion on gate-to-gate times. For example, two flights operating on the same route,
but under a different set of conditions can have significantly different gate-to-gate times,
even if both flights experienced no delay due to airspace or airport congestion. The
potential influence of some of these factors is illustrated in the next section, using three
specific O-D pairs as examples. Some statements on the significance of these factors for
the estimation of the baseline times will be made in section 2.4.
33
2.3 Data
The data used in this thesis were obtained from the Airline System for Quality and
Performance (ASQP) database. The ASQP database is maintained by the US Department
of Transportation (DOT). ASQP encompasses data for the ten major air carriers in the
US. The data are reported by the airlines themselves. The reporting carriers are Alaska,
America West, American, Continental, Delta, Northwest, Southwest, TWA, United and
US Airways.
ASQP reports four time events for each flight: push-out, wheels-off, wheels-on and pushin (Section 2.1). These times are recorded automatically through the Air Carrier
Automated Reporting System (ACARS). In addition to the four time events, ASQP also
indicates for each flight the scheduled departure and arrival times, the scheduled gate-togate time, the actual gate-to-gate time, and the taxi out, taxi in, and airborne times.
It is important to note that gate-holding delays that may be imposed by the Air Traffic
Flow Management (ATFM) system are not included in the actual gate-to-gate times
reported by ASQP since they occur before the brake is released (i.e. the push-out time).
Only ground holding delays occurring on the tarmac after push-out are taken into account
in the data. One potential way of estimating gate-holding delays might be to assume that
any departure delay - defined as the time between scheduled departure and actual pushout - constitutes a gate-holding delay. But this method can result in a potentially gross
overestimation of gate-holding delays, as the delay in leaving the gate may be due to a
late arrival of the aircraft (i.e. delay propagation, in which case the delay would be
double-counted) or to reasons entirely unrelated to the airport or to traffic conditions
(e.g., a delay due to mechanical problems or to late-boarding passengers). This is one of
the principal limitations of the data utilized in this thesis.
The following material illustrates the kind of information that can be extracted from the
ASQP database. The evolution of gate-to-gate, airborne, taxi out, and taxi in times for
three origin-destination pairs during the 1995-2000 period is examined. Data pertaining
34
to the following Origin-Destination pairs were used: BOS-DCA, DCA-BOS, LGA-ORD,
and DEN-SFO. These three specific pairs were chosen to illustrate results for short,
medium, and long-range markets. Note that the statements made in the remainder of this
section apply only to the three routes examined. They do, however, suggest a number of
hypotheses about all the routes examined.
Figure 2.2: Variation and evolution of Scheduled vs. Actual gate-to-gate times for three
origin-destination pairs
Figure 2.2 shows the evolution of annual average scheduled versus actual gate-to-gate
times from '95 to 2000. The average actual gate-to-gate time has increased by about 3
minutes from '95 to 2000 for BOS-DCA and DEN-SFO, and by 12 minutes for LGAORD. In contrast, the average scheduled gate-to-gate time has remained constant for
BOS-DCA over the '95-2000 period; it has increased by 5 minutes for LGA-ORD and by
3 minutes for DEN-SFO. This suggests that although scheduled gate-to-gate time may be
35
increasing over the years (except for BOS-DCA), it may not be increasing as fast as the
6
actual average gate-to-gate time
While the average gate-to-gate time has increased from '95 to 2000, the variability in
gate-to-gate time has also increased, as shown by the increase in standard deviations
computed for the three O-D pairs. This may be due to increasing congestion, which
reduces travel time reliability.
BOS-DCA: Breakdown of gate-to-gate time
92
85
F
80
-
130
120 -
5
110 -
75
70
1996
1995
* Mean Air
LGA-ORD: Breakdown of gate-to-gate time
U Mean
TO
197
1998
O Mean Ti
1999
too0 2000
197
1996
1995
U Mean Air U Mean TO 0 MeanTi
1998
1999
2000
Figure 2.3: Evolution of average airborne, taxi in, and taxi out times from 1995 to 2000
Our data break down gate-to-gate time into 3 segments - taxi-out, airborne, and taxi-in
times- and the evolution of each of these is examined in Figure 2.3.
Overall, gate-to-gate time seems to have increased from '95 to 2000.
-BOS-DCA: Interestingly, from '95 to '97, most of the increase in gate-to-gate time
seems to be due to an increase in airborne time. From '97 to 2000, the gate-to-gate time
remained relatively stable; however, the breakdown of gate-to-gate has not remained
constant: average taxi-out time increased significantly while average airborne and
average taxi-in times decreased.
- LGA-ORD: Average airborne time has remained relatively stable from '95 to '98,
before increasing slightly in '99. While average taxi-out increased by over 4 minutes
between '95 and '98, average taxi-in time seems to have remained relatively stable during
6
This is consistent with Mayer and Sinai's observations [Mayer and Sinai (2001)]
36
that period. From '98 to 2000, average taxi-in and average airborne time increased by
about 1 minute, while average taxi-out increased by another 5 minutes.
Similar analysis can be performed for the DEN-SFO O-D pair.
I
Airborne, Taxi Out, Taxi In: 15th Percentiles
BOS-DCA: Evolution of G2G%ile
80
I
86
86
-
3
- 75
85,
E
S70
6-5
60
+
1998
1997
1996
1995
1%L-
M
1%)
k
2000
1999
e
1995
1997
1996
EoAirl5%ile MTO
1998
15%ile
2000
1999
LITI 15%ilel
Figure 2.4: Annual Evolution of gate-to-gate percentiles
Gate-to-gate times achieved by 10%, 13%, 15%, and 17% of the flights each year are
reported here as 'percentiles'. For BOS-DCA, percentiles have increased from '95 to '97
before slowly decreasing again from '97 to 2000 (Figure 2.4). Over the '95-2000 period,
however, percentiles have increased by about 2 minutes, reflecting the fact that low times
achievable earlier could not be met in later years. It is also interesting to note that there is
only a minor difference in time (about 2-3 minutes) between the 10 h and the 17t"
percentiles.
The individual components of the gate-to-gate times may undergo more
significant changes. For example, the 15 percentile of taxi out time has increased by
20% from '95 to 2000, as seen in the right part of Figure 2.4.
37
Figure 2.5: Directionality
The average gate-to-gate time of BOS-DCA is consistently higher than that of DCA-BOS
(Figure 2.5, left). In fact, the average gate-to-gate time for DCA-BOS is smaller than the
percentile of the BOS-DCA gate-to-gate time for certain months. The same
observation can be made when comparing the 15 percentile of BOS-DCA to the 15th
151h
percentile of DCA-BOS for the same periods (Figure 2.5, right). In part, this is the result
of favorable directional winds in the DCA-BOS direction and suggests the importance of
treating each direction separately.
DEN-SFO: Mean and 15th percentile G2G
200-
190
-
180
170
50140
130
120
a
cn orl \0 O
rl r-
*Mean
r- r- r- 00 W~ W~ 00 a, CN 01ON <=
G2G
0
0
015%ile G2G
BOS-DCA/DCA-BOS:Mean
G2G
95
90 -
7570
{
I
1
MBOS-DCA
*DCA-BOS
Figure 2.6: Influence of Seasonality on gate-to-gate times
38
Figure 2.6 suggests that seasonality may influence gate-to-gate time significantly. This is
shown by the cyclical pattern for the DEN-SFO route. The average and 15 th percentile of
gate-to-gate time tend to be high in January, to then decrease until July, and start
increasing again after the month of July. Different O-D pairs may have different cyclical
patterns.
LGA-ORD 2000- G2G per day of week
BOS-DCA 2000- G2G per day of week
98
97
96
160
t
-9A*700o".
155
1150
E 94
193
P92
145
990
140
89
11
M
T
11
W
1
Th
46.4
3
F
Sat
U Mean ASQPG2G
Sun
---
135M
All
T
W
Th
Sat
Sun
All
U Mean ASQP G2G - Mean Crs G2G
Mean Crs G2G
DEN-SFO 95: G2G Breakdown per
day of week
BOS-DCA 2000: G2G breakdown per
day of week
100-
170
95
160 -
3.-~.-.
90-
-150
.
-
-
65 -1
E-4
120
70100
M
T
W
Th
F
N Airborne U Taxi Out
at
O Taxi In
Sun
All
M
T
W
Th
F
O Airborne 0 Taxi Out
Sat Sun
O Taxi In
All
Figure 2.7: Influence of day of the week on gate-to-gate times
As shown in Figure 2.7, average gate-to-gate time varies slightly depending on the day of
the week. As expected, Saturdays seem to have the lowest average gate-to-gate time for
the three O-D pairs considered. This can be explained by the lower demand for travel on
Saturday and, consequently, the lower number of operations generally scheduled on that
day, which result in less congestion.
Thursdays and Fridays seem to have the largest average gate-to-gate times (and the
largest average airborne, taxi out and taxi in times).
39
While the average actual gate-to-gate time varies depending on the day of the week, the
scheduled gate-to-gate time remains relatively constant for the two O-D pairs shown in
Figure 2.7. This suggests the hypothesis that airlines may not consider day of the week
as an important factor when making scheduling decisions.
Fiaure 2.8: Influence of time of day on gate-to-2ate times
Average actual gate-to-gate time may fluctuate depending on the time of the day as
shown in figure 2.8. For example, for BOS-DCA in 2000, the average actual gate-to-gate
time in period 7 is about 7 minutes smaller than the average in period 6.
Average scheduled gate-to-gate time also varies with the time of day in Figure 2.8. One
may hypothesize that airlines believe that time of the day significantly influences gate-togate times. They may therefore assign different scheduled times depending on the time of
the day.
40
BOS-DCA: Comparison G2G times
300
200 --4 250
00
090
9
8
696
- -
25023
50
1995
*AveG2G
1996
3150
1997
M15%ileG2G
1998
1999
-- MaxG2G
2000
-- MinG2G
LGA-ORD: Comparison G2G
450 S20
400350 ~300 -250
9
E200 144
101140
100-
50m-
3times
1995
0 AveG2G
1996
hh-~
5
14
1997
E]15%ileG2G
1998
MaxG2G
1999
5
2000
-MinG2G
Figure 2.9: Comparison of maximum, minimum, average, and 15 Ihpercentile gate-to-gate
times
The minimum gate-to-gate time reported in the ASQP data has remained relatively
constant over the years for BOS-DCA and has increased by 5 minutes from '95 to 2000
for LGA-ORD (Figure 2.9). The maximum gate-to-gate time has fluctuated significantly
during the '95-2000 period for both O-D pairs. Maximum gate-to-gate times can be as
much as three to four times higher than minimum gate-to-gate times.
This can be
attributed primarily to the possibility of aircraft experiencing very long ground holding
times after pushback.
41
DFW-BOS
MIA-BOS
100%
100% 11
90%
90%
80%
80%
70%
70%
60%
50%50
60%
40%
40%
30%
30%
20%
20%
10%
0%
DCI
%
1995 0%0
1997
2000
UMD82 LIMD83 ElMD88 0A300 EB727 E B757
199
6
MD82
1997
2000
MD83 EMD88 LB727 EB757
767
Figure 2.10: Aircraft fleet evolution
The impact of aircraft type on gate-to-gate time is hard to analyze. Figure 2.10 shows that
there have been some aircraft type substitutions on certain routes over the '95-2000
period. Aircraft type mix has remained relatively stable on the DFW-BOS route. By
contrast, the aircraft mix has changed substantially on the MIA-BOS route, where MD88
and B757 have been replaced by A300 and B767. However, there is so much variability
in the gate-to-gate times within each aircraft type category that there does not seem to be
any clear correlation between aircraft type mix and gate-to-gate time performance.
The examples above show that gate-to-gate time on any given route may fluctuate
considerably. Although several factors (seasonality, day of the week, time of the day,
aircraft type) appear to influence gate-to-gate time, their effect on the overall, year-toyear average gate-to-gate times may not be significant. In particular, due to their periodic
nature, the factors of seasonality, day of week and time of day, may simply be the cause
of fluctuations around the yearly averages. The effect of directionality, however, is
clearly something to be taken into account. For the remainder of this thesis, we will
consider directional Origin-Destination pairs.
2.4 Potential measures of delay
The primary goal of this thesis is to develop a measure that monitors the evolution of true
delays over time. This will involve taking the difference between two times: the actual
42
gate-to-gate time, and a theoretical benchmark, the "baseline", which is yet to be
determined. This approach will ensure that delays are not double-counted (since our
measure will be insensitive to delay propagation), and that the schedule adjustments
made by the airlines (i.e., lengthening of scheduled gate-to-gate times as actual gate-togate times increase) do not influence the metric.
The principal use of these baselines will be for policy purposes. Once developed, they
could be used to monitor the approximate size of delays nationally (if the 27 airport
database is extended to more airports), or at individual airports. They could also be used
to assess whether or not the airport system and the air traffic management system (ATM)
system are keeping up with the traffic on aggregate. Therefore, we are primarily
concerned with identifying long-term trends7 and changes, not the day-to-day fluctuations
that are due to periodic variability or to stochasticity in the system.
The baseline time to be used will be O-D specific and is defined here as the gate-to-gate
time from origin to destination under optimal (non-congested) conditions.
We have
shown in sections 2.2 and 2.3 that gate-to-gate time may be sensitive to the following
factors:
1- Seasonality
2- Day of the week
3- Time of day
4- Weather/Winds
5-
Runway configurations and gate assignments
6- Flight path
7- Aircraft type
8- Direction of travel
9- Congestion of en-route space
10- Congestion of airports and terminal airspace around them
7 i.e.: performing year-to-year comparisons, as well as obtaining rough absolute values
43
Since we will be looking at aggregate changes, we need to differentiate between the
factors that will "average out" over the period considered and those that will not.
Seasonality, day-of-the-week, and time-of-day are of a periodic nature (see section 2.3).
Weather/winds, runway and gate assignments, and flight path are of a stochastic nature.
While from day-to-day or from flight-to-flight they can all make a significant difference,
their impact will cause only small fluctuations around long-term averages computed over
hundreds or thousands of flights. They will introduce error terms in the long-term trends
(e.g., we may have a year with particularly bad or good weather) but overall their
aggregate effects will be those of perturbations. Therefore, we should not be too
concerned with these factors, as they will not make a significant difference on aggregate,
and we are not interested in examining day-to-day fluctuations.
Aircraft type may be significant in the long run, especially for long-range flights. A
switch from non-jets to jets for example could have significant effects. However, all the
data we have used refer to jet flights and the substitution of one jet type for another has
only a small impact on travel times, especially on short-range routes. The pace of changes
in airline fleets during the years examined (1995-2000) was relatively slow and there
does not seem to be a major change in the trends due to this factor. The effects of the
introduction of large numbers of regional jets may, in the future, have a more significant
effect, whenever these jets replace non-jets on specific routes.
Directionality is sufficiently important to necessitate treating each O-D pair as two
distinct routes, A-to-B and B-to-A. Airspace and airport congestion (factors 9 and 10) are
the focus of this research. However, it is hard to determine from the data how much of
the increase in gate-to-gate times is due to en-route airspace congestion and how much to
airport congestion. This will be examined in more detail in Chapter 4.
Some potential candidates to serve as estimates for the baseline gate-to-gate times
include:
.
Average gate-to-gate time:
44
B.. = Ave(G2G 1 )
The baseline for each O-D pair, in this case, would be approximated by the average of
gate-to-gate times on this O-D pair. The sample over which the average would be
computed would cover a full year, to ensure that periodic factors such as seasonality, day
of the week and time of the day average out. The baseline would be the lowest average
observed in any of the years under consideration. (For our data, this would be 1995 in
most cases, since gate-to-gate times seem to have increased over time). A flight will be
considered late if its actual gate-to-gate time exceeds the baseline average gate-to-gate
time'. A crucial drawback of this measure is that the average gate-to-gate time is heavily
influenced by delay whenever congestion is present. Thus, unless a "delay-free" year is
identified for setting the baseline, using average gate-to-gate time as the baseline would
almost certainly lead to serious underestimation of true delays.
Minimum gate-to-gate time:
.
B = Min(G2G1 )
The baseline for each O-D pair would be the shortest observed actual travel time on that
O-D pair, for the sample under consideration. A similar measure has been suggested by
Mayer and Sinai (2001) as an estimate of the congestion-free time9 . The reasoning behind
the use of this metric is that if any flight was able to achieve the minimum reported time,
any other aircraft might be able to reproduce this time in uncongested conditions.
However, it can be argued that this is an overly optimistic estimate as the minimum gateto-gate time could have been the result of a particularly favorable combination of runway
configuration and favorable winds, conditions that might be very difficult to reproduce.
Use of this baseline is likely to lead to the overestimation of true delays.
Percentile of gate-to-gate time:
B1
=
G2G , such that Pr(G2G < B.)
=
p where p is a specified percentile.
Note that use of this estimate as an appropriate baseline will also require that "negative delays" (which
occur when a flight's actual gate-to-gate time is shorter than the baseline) be counted as null delay.
9 Note however that Mayer and Sinai (2001) propose to use the shortest observed travel time on each O-D
pair EACH MONTH. Therefore, their baseline evolves in time.
8
45
The baseline for each O-D pair would be approximated by a percentile of gate-to-gate
times observed on that specific O-D pair. If the percentile used is in the
5 th
_2 0 th
percentile range, this measure could have desirable properties: it would be a realistic
optimal time since a rather significant percentage of flights were able to achieve this
performance; it would be neither overly optimistic nor overly conservative; and it would
cover a broad range of periodic and meteorological
conditions, and runway
configurations. It is important to note that not all percentile measures are appropriate: the
properties described above do not hold if the percentile chosen is too low (overestimation
of delays) or too high (underestimation of delays). Note that the minimum travel time is a
special case of this measure with p=0.
In addition to these simple measures, one could envision estimating the baseline time by
using the following type of modeling approach:
.
Baseline as a function of seasonality, time of the day, and day of the week
Bi, = bo + b * f (time) + b2 * f(dow) + b3 * f(Season)
b0 : O-D-specific constant
b1 : Coefficient associated with time of the day parameter
f(time): Function of the time of day
b2 : Coefficient associated with day of the week parameter
f(dow): Function of the day of the week
b3 : Coefficient associated with seasonality
f (Season): Function of the season
According to the above estimate, each flight would have its own baseline depending on
the periodic conditions under which it is operating. Use of this estimate assumes that
periodic factors -seasonality, time of the day, and day of the week- strongly influence
gate-to-gate time and should therefore be taken into account when deriving the
benchmark. The above estimate would then represent a more realistic optimal time for
each flight, "adjusted" for each given set of conditions.
46
Note that this approach does not include stochastic factors in the baseline estimation
because of the difficulty in obtaining data on these factors and their stochastic nature.
Moreover, including the stochastic terms would render the model less usable and less
informative, as discussed below.
One of the advantages of using this baseline is that we are controlling for periodic factors
that could result in potential discrepancies in gate-to-gate time. The delay measure
obtained in this way- difference between actual gate-to-gate time and the baseline defined
above- would consist primarily of congestion-related delay, as the periodic factors would
have been accounted for in the baseline. However, there are two arguments against using
that estimate for our purposes. First, we have already mentioned that we are not interested
in day-to-day fluctuations and are only looking at long-term trends. Using that baseline
would give us added precision that we do not need. Second, this metric might not lead to
a correct estimation of true delays: one can view seasonality, time of the day, and day of
the week as periodic factors affecting gate-to-gate time in the sense that these factors are
strongly associated with fluctuations in demand levels (scheduled operations). However,
we are not interested in adjusting the baseline to account for the different demand levels
because the baseline's goal is precisely to estimate the impact of those demand levels on
gate-to-gate times. The baseline should therefore be independent of demand levels
because it is intended to be used to estimate the inefficiencies in the system that are
created by excessive demand and lack of proper infrastructure to accommodate it.
It is a challenging task to define a baseline that will approximate a congestion-free time
while being conservative enough that it accounts for a variety of runway configurations,
flight paths, and wind directions. Given the above discussion, it seems that using a
percentile measure in the 5-20% range to compute the baseline would be most
appropriate. Chapter 3 examines in greater detail which percentile to choose and the data
that will be used to derive this estimate.
47
48
CHAPTER 3: BASELINE ESTIMATION
Chapter 3's goal is to describe the methodology used to derive baseline times for the 618
O-D pairs under consideration. Section 3.1 details the methodology used. Section 3.2
shows two applications for the use of baselines: the calculation of true delays; and the
comparison of the evolution of true delays versus delays relative to schedule.
3.1 Baseline time estimation methodology
in the 5-20th
It was argued in Chapter 2 that it is appropriate to use a percentile measure
percentile range as a means of estimating the baseline time of a specific O-D pair. The
baselines are supposed to approximate "congestion-free" gate-to-gate times. They are
also supposed to be "achievable", meaning that a substantial percentage of flights
operating on that O-D pair should be able to achieve a similar performance.
If the percentile chosen is in this range, the resulting baselines will have these desired
properties. Percentiles in that range are low enough that they will yield baseline times
that do not encompass significant delays, making them a good approximation of
"congestion-free" times. The associated baseline times are also long enough to be
49
achievable by many other flights under a range of meteorological conditions and runway
configurations.
The baseline time for a given O-D pair (i,j) using the x'h percentile was calculated as
follows: (See Appendix A for more details on the notation used)
Bx=M IN (AF 1 -(95), AF '(97), A2 Il'(00)).............................(3.1)
with
AI' (95)= (1%' (1,95)+ lJ' (4,95)+
(7,95)+ I7 (10,95))/4......... (3.2)
A1I'c (97) (J -((1,97)+ Pijx (4,97)+A
1 (7,97)+,-(10,97))/4..........(3.3)
A<1 (00)= (JA (1,00)+ P) (4,00)+ I') (7,00))/3.........................(3.4)
where
B-': baseline time for O-D pair (ij) using the xth percentile
<A(m,y): gate-to-gate time associated with the
xth
percentile of gate-to-gate time on (ij)
in a given month m for year y
A<,(y): average gate-to-gate time associated with the
xth
percentile of gate-to-gate time
on (ij) in year y
Note that in the calculation of the baseline, only three months (January, April, and July)
were used for the year 2000 because of the unavailability of data for the month of
October 2000 at the time of the study. To ensure that this approximation would not skew
our results, we also computed the average gate-to-gate time for all available months in
2000 (January through September, and November 2000)10. Since no significant difference
between the results was found, we concluded that this approximation would not weaken
our findings.
We saw in Chapter 2 that day of the week, time of the day, and seasonality might be
factors influencing the gate-to-gate time. However, it was argued that these factors may
10 At this time, we do not have the October 2000 file
50
not have a systematic influence on long-term averages. Therefore, we will not consider
them explicitly in the baseline derivation.
3.1.1 Sensitivity Analysis
In this thesis, we chose to use the fifteenth percentile of gate-to-gate time in order to
compute the baseline. It was decided that the fifteenth percentile would be suitable, as it
offers a reasonable trade-off between the objectives of capturing both "congestion-free
times" and "achievable times". The fifteenth percentile encompasses little significant
delay, yet it yields a sufficiently conservative estimate of travel time.
We used a sample of the 26 O-D pairs originating at BOS to illustrate the sensitivity of
the baseline to the percentile chosen. This sensitivity analysis also provided an
opportunity to test our choice of the fifteenth percentile. We started by calculating
individual baselines for each of the 26 O-D pairs originating in BOS (according to
th and 2 0 th
through (3.4)), successively using the 5 th, 7 th, I 0 th, 13 th, 1 5 th, 17
equations (3.1)
percentile. Results are shown in Appendix B. To compare efficiently the results obtained,
we aggregated the individual O-D results by computing a "weighted baseline" for each of
the seven percentiles used. The weighted baseline consists of taking the weighted
average" of the 26 O-D baseline times, as shown in equation 3.5.
WBBOS
(Z B=BS,
TF=BOSJ (00)) /(
TFi=BOSJ (00)) ...................... (3.5)
where
TFi=OSJ(O)= F>=BOSj(1,OO)+F'=BOS~j (4,00)+Fi=BOS, j(7,00) ....
''...........(3.6)
and
Fi.BOSj (m,y)z number of flown flights in month m of year y on route (BOSj).
"x " is the value of the percentile used to calculate the baseline.
" Weighted by number of flights flown
51
The sensitivity of the weighted baseline to the percentile chosen is shown in Figure 3.1
below.
Figure 3.1: Sensitivity of the BOS weighted baseline to the percentile chosen
The difference between the weighted baseline obtained using the lowest percentile (fifth)
and the highest one (twentieth) is only of the order of 5%. This suggests that any of the
percentiles in the 5-20 range, including the fifteenth percentile, would be appropriate for
use in the baseline estimation. It is important to remember that the baselines will be used
as benchmarks against which delays can be consistently measured over time. In that
respect, the exact value of the baseline is not especially critical to our measure of the
evolution of true delays.
The exact value of the percentile to be chosen for an "optimal' baseline is not an issue
that we will consider further in this thesis. Note that the methodologies outlined in the
remainder of this thesis could be used with any percentile in the 5-20 range.
3.1.2 Results
Figure 3.2 shows the baseline times, estimated using the fifteenth percentile, for all the
O-D pairs considered.
52
ORIGIN AIRPORT
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
ATLIBOSIBWIICLE JCLT
148 98 921 561
134
70 921 112
92
75
60 68.5
891 1051 62
78.8
75
51 121 70
bb.b
77 114
77.5
125
72
83 50
89
DEN 176
I- DFW 123
0 DTW 100
EWR * 117 '
z FLL 1961
0 IAD 1881
IAH 1112
LAX 1 262
LGA 114 ,
w
03 MCO
73
MEM
66
MIA
96
MSPI 142
ORD1 104
PHL 105
PHX 223
85
61
65
252 210 1771 2031
2291 183 1571 1551
117i 83 43i 91.3 '
'
68F,
771 92.2
140
156
101
177
63.(
83
2321 1761 161
3521 3131 285
521
1661
172
182
1721
1421
471 771 89.8
1191 131 180.51
105 90.2
139 1521 10(
1431 107
1101 69 1051
701 371 671 7841
319
2624
ICM-CVG
DCA DEN DFW DTW EWdFLL IAD IA LAX LGA IMCoIMEMMIA IMSPIORDIPHLIPHX IPIT ISFOTPA
801 721 97.41 153 1091 1031 1261 97.41 93.31 1031 2291 1291 76.71 63.5 101 135199.31 1111 191190.31 253177.8
97 111 74.61 209 1981 99.81 58.21 1641 75.81 2051 3031 49.81 1541 154 179 1481 120 601 2731 83.31 312 160
161 271 50.5 116
1401 129194.5 37
52.5 282 121
13 7
. 1791 15 77 79.4
73 L
51.31 66.2 , 154 1411 39.81 82.81 154
145 29 83.2 131 94.5 157194.1161.31 72 212M 250 133
98.31 861 77i 1101* 129193.2
65.6 167 1321 84.31 94.4 1051 631 125 2491 -i-----821 i 2171
72.91e 2661 85.8
- i
t t tI
I
64.5 148 1331 45.31 90
91 122
121
93.81 59.5 741 1981 40.1
-118
56.1
102
1
37
109 1191 70.4 1431 91.51 58 921 1871 571 238 117
152
58 69
56.7 1
54.5 113 1071 136 124190.8 43L
50
119
166 11
235 2101 136 239 108 1361 2221 931 1881 131 206
168 233M
207 1691 176 561 1661 211 1551 79.5 174 136 1291 1951 1241 1651 187 145
1461 1:
1811 1
1
59
.
150
149
147
98.51
16717.71 1461 2411 99.81 1471 98.81 1691 88.31 601 921 2091 52.51
50
85 3
841 95515591 1961 185
256 67.3 299 143
107
146 160 157,
141 10251
146
4(
160 147
149 73.8
135
153 266 59.5 112
133
89.5 43 224 46.7 271 116
175 209 135
123 52.51 160 205 146 1767
148
1371 1941 1391 1681 206 122
129 1801 273 334 314 304 11
297 229 314 217 239 3231 69.31 2891 68.3 289
791 95.7
1341 .$160 ' 141 107 38 %
65.3
195 ,
UI" 141
53.1
-I
53.1 .
195
1151 1081 121 188 137 1401 146143.7 118 120 259
1041 50.3
1711 -41371 1321 2261 1221 2881 32.9
~~~I- - I
197 151 11
1371 105 , 84.81 1401 159
72.8 121 119 73.2 104 15C
2181 108
139
211
1331
149 162
124
140 129 273 . 162 50.
1971 162 1491 2451 1471 303E
192 160
1111 2'
1011 145 100 1261 98.5 16
70.81 154 167 1201 1941 187
- -117 180 79.5 222 147
64 601 106 123 1181 59.5 1261 171 1021 1321 2181 127 151188.81 1751 64
681 83 3 46 3 I1891 1681 80
144148211741 2771418 12 9 124 149 133 102
2-rn 55.3 292 133
252 101
30216,
97.5 136 2341 302
268 150 64.3
259
180 200 290
2491
6
SFO 286 363 329 303 314
TPA1 74 179 128 139 85.3 119
141 , 208 285 351
269
113
127
185
130
143
155
150 106
32 2 249 343 225
31422 8 65.3
46 121 11 0 2581 160 32 .9 98 46.5 172
Figure 3.2: Baseline Times Der O-D Dair
58 2
249 339
138 141
1
9F;9
12
ORIGIN AIRPORT
ATLBOS BWI CLE CLT CM CVG DCA DEN DFW DT
ATL
12.22.1 15.5
15.8
BOS
19.8
BWI
15.0 13.4
CLE
.06 15.8
CLT
12.1
17.1
18.0
19.7 13.2
12.2
1.8
.8
17.8 10.5
16.0 20.1
18.6
19.2
12.3
11.8
3.4 14.2
13.9
16.8
15.
18.68
16.4
12.8
15.9
12.4
15.4 14.4
20.4
10.7
12.2
10.2
11.4
12.6 21.1
12.0
11.5
13.4 12.3
10.6
12.51 20.9
9.2 20.2
11.1
13.2
1.
11.1
10.5 20.9
17.0
8.9
15.7 13.0
14.6
17.1
17.9
15.4
9.5
18.6
19.6
19.6 19.2 18.6 14.9
11.9
17.1
20.6
16.2 15.9
24.6
13.4
11.6
22.3
31.4
16.4 13.9
19.4 16.0
16.7
23.4
14.5
15.4
12.1
14.4 12.4 13.2
13.2 10.7 13.1
12.6
13.3
13.0 14.7
19.7 13.5 21.5
17.9
15.5 20.5 18.4 15.3 17.3 20.7
11.9 20.5 17.9 17.8 19.7 10.2
13.9 9.5 15.8 23.1
11.3 9.9 17.1 8.9
9.9
28.2
24.8 17.3 18.2
11.1 12.4 10.4 9.6 12.8 12.4
MIA
14.4 18.7 16.0 17.1
10.2
MSP
19.0 20.9 19.9 18.5
ORD
PHL
PHX
PIT
SFO
TPA
20.5
20.1
19.5
15.1
24.7
12.7
9.9
22.1
23.0 22.4
15.5
14.1 20.7
14.1
15.0
15.81
17.1
14.6
16.8
14.0
14.1
17.7
15.5
18.8
18.3 20.6
5.7
24.6
18.1
21.7
16.3
10.3
8.9
16.2 20.7
23.7
15.3
14.5
15.4 24.5
14.2
14.0
10.3
11.6
21.0 15.0
15.5
16.0
18.1
18.2 20.3
19.1 27.6
17.6
22.1
17.1
18.6 13.9
9.4
11.6
15.6
14.6 16.8
11.4
10.6
12.0
12.2 17.3
17.3
13.3
14.9 17.8
13.1
10.1
15.0
16.1 25.2
13.7
17.3
13.3
16.7
8.6
9.6
9.7
20.5
17.3 12.7 20.3
22.3
12.5
18.8 16.5
23.4
19.8 20.2
13.1
22.5
16.9
18.6
10.6
9.9
17.5
9.9
21.2
21.1
13.0
14.7
21.4
11.0
27.3 21.4
17.7
27.5
18.2 12.9
31.1
21.9 7.3
21.5
10.4
26.6
18.3
33.9
12.8
17.0
23.3
11.6
11.0
13.3
10.8
26.3 19.8 13.1
16.7 15.6 14.0
13.2
21.7 11.7
19.0 17.9
7.8
21.5 10.1
20.9
22.4
13.5
16.2
19.9
15.1
12.7
17.4
22.2 16.0
17.7 20.2 18.5
18.3 20.6
14.2 10.9
20.4 24.4 25.4
15.0 12.7 13.2
Figure 3.3: Average "true" delays per O-D pair in 2000 (min/op)
18.4
15.0
12.2
19.5
10.2
19.5
12.11
12.9
15.7
16.4
13.3 13.4 20.6
17.1
14.0
18.6 20.1 22.6
13.7
17.4
16.0
19.4
18.9
21.2
12.9
27.1
14.1
16.3
18.9 19.4
7.9
9.4
11.9
11.5
15.0 16.7
17.6
13.9
9.6
14.7 IM
31.1 11.9 14.4 13.7
22.3 13.5 14.71 16.3
18.7 16.0 15.1 15.7
20.5
10
12
.
13.3 22.2 16.4
20.4
16.4 20.4
14.8 15.4
15.9
16.3
15.4
1
.
10.0
18.3
12.5
13.9
22.5
19.0 22.7
17.9
12.9
11.2
13.21
11.2
13.6
11.5 15.2
14.2
15.
12.4
21.0
12.5
14.4
13.3 14.8
13.6 13.1
16.7
17.8
12.4
10.4
10.4
21.1
13.9
20.8
12.1
iMCO 12.6 23.4 12.3 11.0
10.7
MEM 11.2 17.3
23.9
22.4
24.2
15.4
27.2
21.9
16.6 22.2
13.5
14.4
16.6
16.0
10.7 15.5 10.5
22.4 12.1 13.1 21.8
12.5 17.6 27.3
16.1 22.7 15.3 16.1 11.71 12.6 21.91
9.7,@
18 15.3 17.7 17.81 17.0 21.4
13.2 13.6
15.0 25.3
20.9 20.0 19.8 13.3
1
14.8
16.3
LGA
22.3 23.3
7.7
17.1
LAX
19.9 20.8
1.8
14.4
17.9 25.2
7.1
14.1
17.8
14.3
16.3
16.
22.2
23.9
18.0 11.9
21.1
16.0
12.0
14.7
15.1 23.1
14.2
15.2 25.0
14.8 19.5 28.4
ORD PHL PHX PIT SFO TPA
15.8
15.5
13.4 20.8
15.7
14.7
IAH
13.0
10.3
19.4
17.9 18.1
MEM MIA MSP
23.9
21.7
14.7 14.1
IAD
12.4
14.6. 22.2
1. 6
17.1
FLL
22.8
22.4 23.8
15.6
11215.7
16.3
15.0 15.0
13.2 12.8
9.8
14.
17.2
13.9
10.1 8.5
11.0 20.8
14.0 12.3
16.2 12.1
12.8 30.5 12.5 11.3
17.0
16.7 17.0
11.4
18.3 24.0 17.8
9.8
DCA 12.0 12.1
DEN 19.0 18.1 2.3 18.5
w DFW 15.5 21.4 14.1 17.1
SDTW 15.9 17.0 13.7 14.5
EWR 19.7 13.6
FLL IAD IAH LAX LGA MC
32.9 20.4 23.3
18.7
15.7
12.8
9.8
1.
14.8
11.8
16.8
13.0
CMH 12.7 12.51
CVG
19.6 13.4
EW
25.7 21.0
17.1
21.1
18.2 12.7
32.7 12.8
20.1
11.3
11.8
7.1
11.3
8.1
17.7
18.4 17.2 19.5
18.0 19.2 18.4
12.8 10.0
12.8 12.7
22.5
11.2
The O-D baseline times shown in Figure 3.2 are computed from expression (3.1). It is
interesting to note that in the great majority of cases (63%), the minimum of the
quantities included in (3.1) is the fifteenth percentile associated with 1995. The second
higher number of minima is associated with 1997 (27%) while only a small number of
entries (10%) is associated with 2000. This suggests that there was an overall upward
trend in transit times between 1995 and 2000, a point to be noted in a number of instances
later in this thesis.
3.2 Application: Evolution of O-D delays from 1995 to 2000
3.2.1 Calculation of O-D delays
Having established the baselines, we can now calculate "true" delays for each O-D pair.
The average true O-D delay in each year can be computed as the difference between the
average gate-to-gate time in that year and the baseline time.
The average O-D delay on route (i,
D)!(y)= AG(y- B 5
j) in year y
is defined as:
. .. .. ... .. .. ... .. .. .. .. ... .. .. ... .
(3.7)
Note that the average O-D delay in equation (3.7) is computed by taking the average of
gate-to-gate time in year y minus the baseline time. This is equivalent to taking the
average of individual flight delays in year y, where an individual flight delay is defined as
the actual gate-to-gate time of this flight minus the baseline. Flights incurring gate-togate times smaller than the baseline incur a "negative" delay.
True delays incurred in the year 2000 are shown for each O-D pair in Figure 3.3. The
delay is in minutes per operation.
55
"True" delays in 2000 on the routes considered range from about 5 minutes to 34
minutes per operation. Over the months of January, April and July 2000, 94% of the 618
routes considered experienced an average delay per operation of at least 10 min; 56% a
delay of at least 15 minutes; 21% a delay of at least 20 minutes; and 4% a delay of over
25 minutes.
In order to analyze their evolution, O-D delays were calculated for each O-D pair in
1995, 1997, and 2000. We then aggregated the data by forming the overall weighted
delay, which is defined as the weighted average of delays incurred on each of the 618 0D pairs (3.8). Details are shown in appendix B.
WDALL (y) =
i
j#i
.......................... (3.8)
,
TF,(y)* D (y)((ZTF(y))
i ji
Evolution of the weighted average delay from 1995
to 2000
18
- 16
E14
12
10
8
> 6-
0
1995
1997
2000
I
Figure 3.4: Evolution of the weighted average "true" delay from 1995 to 2000
The overall weighted average of "true" delays on the 618 O-D pairs has increased from
11.1 minutes per operation in 1995 to 16.9 minutes in 2000. This represents an increase
in "true" delay of about 52%. Routes on which true delays have increased most during
that period are those originating in PHL, IAD, CVG, LGA, and BOS on which delays on
average have increased by more than 78%.
56
Delay increase distribution from 1995 to 2000
80
u)
-h
7570-
- --
65-
~60-
0
45-
~40~-35030fl25-
E 20 -1
Z
S151050
<0%
0-10%
10-20%
20-30%
30-40%
40-50%
50-60%
60-70%
70-80%
80-90%
90-100%
>100%
n/a
Percent increase in average minutes of delay per operation from 1995 to
2000
Figure 3.5: Distribution of the delay increase between 1995 and 2000
Figure 3.5 illustrates the magnitude of the increase in delays at the O-D pair level'. Only
57 of the 618 O-D pairs experienced a drop in the average "true" delay per operation in
the 1995-2000 period. All other pairs experienced an increase; 75 pairs saw delays more
than double from 1995 to 2000.
3.2.2 Comparison with DOT statistics and delay relative to schedule
The next step consists of examining the implications of using the "true" delay definition
versus alternative delay definitions such as "delay relative to schedule" and "delay
relative to scheduled transit time".
Average delays relative to schedule are computed as follows for each O-D pair. The total
delay on an O-D pair (i,
j) during
year y is the sum of the difference between actual and
scheduled arrival times for each flight in the months of January, April, July, and
October' 3 . The total delay is then divided by the number of flights flown in those months.
12 n/a includes routes that were not flown either in 1995 or 2000
13 In 2000, only the months of January, April, and July are used.
57
DRSJ (y)
=
(
Y (ActualArrivalTime - ScheduledArrivalTime))/IT; (y) ........... (3.9)
flighse(ij)iny
In order to allow for an efficient comparison, we aggregate delays relative to schedule
and calculate the weighted average of delays relative to schedule over all 618 O-D pairs.
WDRSL (y) = (Z
Y TF, (y) * DRSf(y)) /(I Z
i
i j#i
TF (y)) ............................. (3.10)
j
Similarly, average delays relative to scheduled transit time are computed for each O-D
pair. The average delay relative to scheduled transit time on an O-D pair (i,
j) during year
y (DR TT1J) is the sum of the difference between actual and scheduled gate-to-gate times
for each flight in the months of January, April, July, and October
4
of year y, divided by
the total number of flights flown in those months in year y.
DRTT(y) =(
Z (Actual _G2GTime -Scheduled _G2GTime)) / TF1j(y) ....... (3.11)
flightse(i,j)iny
We also calculate the weighted average of delays relative to scheduled transit time over
all 618 O-D pairs as follows:
WDR TTALL (Y)
=(
(
I
T, ( y) * DR TTi(y)) /(I I T, (y)) ..........................
j~i
i
(3.12)
j
A comparison of weighted average "true" delays, delays relative to schedule, and delays
relative to scheduled transit times is shown in Figure 3.6.
14
In 2000, only the months of January, April, and July are used.
58
Figure 3.6: Comparison of overall average true delay versus other delay measures
Figure 3.6 shows that on aggregate, both true delays and delays relative to schedule have
increased over the 1995-2000 period. In 1995, true delays were larger than delays relative
to schedule by about 4 minutes; in 2000 they were larger by about 5 minutes. It seems
that the gap between true delays and delays relative to schedule is remaining rather stable
over the years. Overall, average true delays seem to be about 40% to 60% larger than
delays relative to schedule.
Average scheduled transit time has increased on average by 10.5 minutes from 1995 to
2000, based on the analysis of the 618 routes under consideration (See Appendix B for
more details). This is an illustration of the point made in Chapter 2 about airlines
"adjusting" their schedules constantly to achieve better on-time performance.
Figure 3.6 shows that in all years considered, the average delay relative to scheduled
transit time was slightly negative on average, which means that actual gate-to-gate time
was on average shorter than scheduled gate-to-gate time. This observation suggests that
airlines are good at predicting gate-to-gate times. However, Figure 3.6 also shows that
flights arrive on average 7 to 12 minutes behind schedule. One can therefore conclude
that although airlines seem to be able to accurately predict gate-to-gate times, they are not
good at predicting departure times, which results in delays relative to schedule.
59
The DOT definition of on-time performance implies that any flight arriving within 15
minutes of its scheduled arrival time is considered to be on time. Using a similar 15minute rule, we calculated how the percentage of on-time flights would change if we
used the "true" delay definition and the delay relative to scheduled transit time definition
instead of the delay relative to schedule definition. Under the "true" delay definition, a
flight would be on time if the gate-to-gate time it incurred was not greater than the
corresponding baseline by more than 15 minutes. Under the delay relative to scheduled
transit time definition, a flight would be on time if the gate-to-gate time it incurred was
not greater than the corresponding scheduled gate-to-gate time by more than 15 minutes.
Results are computed for each O-D pair and are then aggregated using weighted
averages.
Figure 3.7: Sensitivity of on-time performance statistics to the delay definition used
Using the "true" delay definition yields considerably lower on-time performances in all
years. If the "true" delay definition had been used in 2000, only 54% of all flights
operating on the 618 O-D pairs would have been considered "on-time".
60
In this chapter, we established a methodology for the estimation of true delays on a given
O-D pair. It was proposed that for national policy purposes, it may be appropriate to use
the fifteenth percentile as a robust estimate of the baseline transit times. This
methodology can be extended to the entire national network.
In Chapter 4, we will outline different procedures to attribute the O-D true delays to the
origin and destination airports.
61
62
CHAPTER 4: ROLE OF AIRPORTS IN
GENERATING DELAYS
One of the challenges remaining once O-D-specific delays are computed is to attribute
these delays to airports. Most of the delay on an O-D pair occurs at the origin or the
destination airport, as airports typically constitute the bottleneck in the air transportation
system. Some of the problems exacerbating congestion and delays at the US airports
include the absence of demand management measures as well as the reduction in capacity
that results from bad weather.
Section 4.1 will examine different methodologies that can be used to attribute O-D delays
to the relevant airports. Section 4.2 will present an analysis and discussion of the results
obtained in Section 4.1.
4.1
Estimation of airport delays
In this chapter, we are only concerned with allocating O-D delays to the airports of origin
and destination. Many methods can be used to do so. Two methods are examined in detail
in this chapter.
63
4.1.1
4.1.1.1
Method A
Step Al
In Method A, it is assumed that O-D delays are due exclusively to the airports of origin
and destination. We will initially assume that the origin airport and the destination airport
both contribute equally to the O-D delay (Step Al). Although this is a crude
approximation of what happens in reality, this simplification will allow us to obtain a
preliminary estimate of the extent of congestion at each airport.
Half of the delay on any given O-D pair is therefore attributed to the airport of origin, and
is called departure delay. The other half is attributed to the destination airport and is
called arrival delay. In order to calculate the average origin delay at a given airport a
(OrgADl,(y)), the weighted average of the departure delays occurring at this airport is
computed through (4.1).
OrgAD1,(y)=0.5* (Z
Di(y) *TF(y))/(
TFI (y)).........................(4.1)
Similarly, the average destination delay at a given airport a ( DestAD1, (y)> is a weighted
average of the arrival delays occurring at airport a:
DestADla(y)=O.5* (
D " (y) * TF, (y)) / (
TF,, (y))........................(4.2)
ii
Finally the average overall delay at airport a (A, 1(y)) is the weighted average of the
average origin and average destination delays at that airport15 :
In principle, taking the weighted average should be the same as taking the average of the origin and
destination delay at each airport, since the number of arrivals at an airport should be the same as the
number of departures. However, in our case, because we are only considering flights operating between 27
airports, not all departures and arrivals are represented. Moreover, the data set has gaps, since only the
months of January, April, July and October were used.
15
64
AA (y)= [ OrgADla(y)*
Y TF
DestAD 140y*
(I TF. (y)) +
(y TF, (y))]
(y )+Z TF (y)) ] ..............................................................
(4.3)
i
i
Step Al is described in Appendix C in greater detail.
For the years 1995, 1997, and 2000, Step Al yields Table 4.1, which allows for a
preliminary comparison of the evolution of delays at each of the 27 airports under
consideration. Table 4.1 indicates estimated delay per airportoperation,not perflight.
I
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
DFW
DTW
EWR
FLL
lAD
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
PHX
PIT
SFO
TPA
__
A (Step Al)
AIRPORT DELAYS 1997
__METHOD
AIRPORT DELAYS 1995
ORG95 IDEST95 |ALL95
5.7
5.6
5.6
5.6
4.9
4.6
5.0
4.9
4.7
4.6
4.4
4.4
4.7
4.2
5.2
4.6
5.6
5.6
5.9
6.6
5.9
5.6
7.1
6.0
4.8
5.6
5.3
4.8
5.5
6.1
5.7
6.3
6.2
5.2
4.8
5.5
4.7
4.8
6.5
6.4
5.9
5.4
5.5
5.9
5.4
4.6
5.0
5.1
5.2
4.5
5.9
7.1
4.7
5.2
5.5
5.51
ORG97
5.6
5.6
4.8
4.9
4.6
4.4
4.5
4.9
5.6
6.2
5.8
6.6
5.2
5.1
5.8
6.0
5.7
5.1
4.7
6.4
5.7
5.7
5.0
5.0
4.9
6.5
4.9
5.5
IDEST97
5.9
7.1
5.0
6.0
5.4
5.4
6.2
6.3
6.3
7.5
6.5
9.0
5.4
6.3
6.2
7.3
7.7
5.5
5.9
6.8
6.6
6.5
7.2
6.4
5.4
7.3
5.7
6.61
ALL97
7.6
7.0
4.6
6.0
5.7
5.5
6.3
5.4
6.0
7.6
6.4
7.8
6.2
6.1
6.4
6.9
6.0
6.2
5.8
7.1
7.0
7.2
6.5
5.7
5.3
7.0
5.7
6.6
AIRPORT DELAYS 2000
DESTOO IALL00
8.3
8.7
8.5
9.9
10.7
10.3
7.1
6.6
6.8
7.7
7.5
7.6
7.3
6.9
7.1
6.4
6.6
6.5
8.7
8.0
8.3
7.7
6.6
7.2
7.1
8.4
7.7
8.2
7.6
7.9
8.4
7.8
8.1
11.4
9.6
10.5
8.0
8.3
8.1
9.4
9.1
9.3
8.3
7.6
8.0
7.9
8.6
8.2
11.0
9.2
10.1
7.3
7.4
7.4
6.4
6.4
6.4
8.0
7.7
7.8
8.1
8.7
8.4
8.5
10.3
9.4
11.1
9.5
10.3
7.3
7.7
7.5
7.5
7.0
7.2
7.8
10.5
9.1
7.3
6.7
7.0
8.4
8.4
8.41
ORGO0
6.7
7.1
4.8
6.0
5.6
5.4
6.2
5.8
6.1
7.5
6.5
8.4
5.8
6.2
6.3
7.1
6.8
5.9
5.8
6.9
6.8
6.9
6.8
6.0
5.3
7.2
5.7
6.61
Table 4.1: Average airport delays (min/op) obtained using Step Al
According to Step Al, the airport with the highest overall delay incurred on average 10.5
minutes of delay per operation in 2000. The airport with the lowest overall delay incurred
on average 6.4 minutes of delay per operation in 2000.
65
4.1.1.2
Sten A2
The accuracy of Method A can be improved by relaxing the simple approximation made
in Step Al. The airports of origin and destination are no longer assumed to contribute
equally to the O-D delay. Some airports are more sensitive than others to increased
traffic, bad weather, and congestion; the model can be improved by taking this into
account. In Step A2, the attribution of the O-D delays depends on the relative weights of
the airports of origin and destination.
Each O-D delay is allocated between the origin and the destination airport according to
the relative weights of these airports. The procedure followed is iterative. Initially (first
iteration), the weights (CORG (y), CDES, 1(y)) are taken to be a function of the origin
delay and destination delay calculated in Step Al:
CORG...
(y) = OrgAD1 (y) /( DestAD 1,(y) + OrgAD, (y) ).............(4.4a)
CDESiite__ (y) = DestADl , (y) /( OrgADl, (y) + DestADIl(y) ).............(4.5a)
In each succeeding iteration, the relative weights will be a function of delay results
obtained in the previous iteration, as given in equations (4.4b) and (4.5b).
(y) /( DestAD2 jjterk(y) + OrgAD2 iterk (y) )..(4.4 b) 16
CORG
(y)
OrgAD2
CDES1 1C
(y)
DestAD2 /,er=k (y) /( OrgAD2i,.,k (y) + DestAD2 jjierk(y)
rk
)..(4.5b) "
The departure delay on an O-D pair (DepD j,.,-k(y)) is calculated by equation (4.6) and
is attributed to the origin airport.
DepDijjtrk(y) = CORG
6
OrgAD2Jte~
Ier=k (y)
DO ...................................................
(4.6)
(y) is to be determined in equation (4.8)
" DestAD2,jiler-k (y)
is to be determined in equation (4.9)
66
The arrival delay on an O-D pair (ArrDi,,.k(y)) is calculated by equation (4.7) and is
attributed to the destination airport.
ArrD
(y) = CDESiiier=k(y) * D I .................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(4.7)
The origin delay at a specific airport a (OrgAD2,j,,,
(Y))
is then obtained by averaging
the departure delays attributed to this airport, using (4.8).
OrgAD2aiher=k(y)= (
DepDIer k(y) *
TF, (y)) / ( ( TF1 (y))........................(4.8)
Similarly, each airport's destination delay (DestAD2
(jte/k(y))
is computed by averaging
the arrival delays attributable to that airport, as shown in (4.9).
DestAD2a,ier=k(y)=( I
ArrD
(y
* TF, (y))/(
TF,(y)) ...................... (4.9)
The procedure is then iterated until "convergence", as shown in Figure 4.1.
The average overall delay is then computed by taking the weighted average of the origin
and destination delays at each airport (4.10).
Aa 2(y) = [ OrgAD2, (y)
(TF
a (y)+
[
*
ITFaj(Y))+
DestAD2,(y) *
(I
TFia(y)) I
TFia(y)) ].................................................................(4.10)
I
67
Compute
CORG~jie= (y)
CDESije= (y)
Compute
CORGEk (Y)
Compute
DepD ltd= (y)
Compute
OrgAD2jter~k(Y)
CDES~jie~
ArrDij~k(y)
DestAD2(,ier=k (Y)
(y)
Ak
I
FN
CHECK IF
7
IOrgAD2 ajiur: I (Y)
- OrgAD2 ,i,-
-(Y) <=0.001
AND
IDestAD21 1fr (y) - DestAD2 aitei
k1(y) I<=0.00 I
OrgAD2, (y)
OrgAD2 .,.,
DestAD2, (y)
DestAD2,Jl,'k (Y)
(y)
Compute A. 2 (y)
Figure 4.1: Step A2 - Description of the iterative process
Airport delays in 1995, 1997, and 2000 were thus computed, as shown in Table 4.2.
68
METHOD A (step 2)
AIRPORT DELAYS 1995
nRG95;
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
DFW
DTW
EWR
FLL
lAD
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
PHX
PIT
SFO
TPA
DlEST95
6.0
5.7
4.4
4.6
4.0
3.6
4.0
4.8
5.3
6.4
6.5
8.6
4.2
4.6
5.1
5.4
6.9
4.2
3.5
7.3
6.3
5.5
5.5
3.7
4.9
5.9
4.1
55s
|
IALL95
5.7
5.5
3.8
4.3
3.7
3.1
3.0
3.5
5.6
7.8
5.9
6.7
5.3
r.~t
4.1
6.6
7.2
5.0
5.4
3.8
7.0
5.4
6.2
4.0
4.6
3.6
8.7
4.8
5.61
AIRPORT DELAYS 2000
ALL97
OR0
DEST97
DESTOO IALLUU
8.7
8.9
8.5
7.1
8.7
5.5
12.2
12.8
11.6
7.6
7.4
7.8
6.1
5.6
6.7
3.4
3.2
3.5
6.8
6.4
7.2
5.5
5.4
5.5
5.9
5.2
6.5
4.6
5.0
4.3
4.8
4.8
4.9
4.3
4.3
4.4
8.3
7.8
8.9
5.9
6.0
5.8
5.4
4.3
6.6
4.8
4.0
5.6
6.7
8.2
5.2
5.4
5.1
5.7
7.5
6.9
8.1
8.7
8.7
8.6
8.0
7.3
8.6
6.5
6.5
6.5
13.3
11.8
14.8
10.5
9.4
11.5
6.8
6.4
7.2
4.7
5.5
4.0
0
-r
10.0
10.2
9.9
5.8
5.9 ES9 5.6
7.7
7.1
8.4
5.9
6.1
5.8
8.0
9.0
6.9
7.5
7.1
7.9
12.3
10.6
14.1
7.4
6.0
8.8
5.8
5.7
5.8
5.0
5.6
4.5
4.5
4.3
4.6
4.7
4.8
4.6
6.9
6.5
7.2
7.0
7.3
6.7
8.4
9.1
7.8
7.1
7.5
6.7
10.1
11.8
8.4
6.9
7.4
6.3
12.7
11.3
14.1
7.5
7.1
8.0
6.5
7.2
5.8
5.1
4.4
5.8
5.9
5.2
6.5
4.1
4.0
4.3
9.6
12.6
6.7
7.6
7.2
8.0
5.3
4.5
6.1
5.0
5.1
4.9
8.4
?8. 4
7.7
I.4
6.6
5.5
AIRPORT DELAYS 1997
0RG97
5.8
5.6
4.1
4.4
3.9
3.4
3.5
4.1
5.4
7.1
6.2
7.6
4.7
4.3
5.9
6.3
5.9
4.8
3.6
7.1
5.9
5.8
4.8
4.1
4.3
7.3
4.5
5.5
Table 4.2: Average airport delays (min/op) obtained using Step A2
Comparison of Table 4.1 and Table 4.2 shows that:
" At the aggregate level, both Step Al and Step A2 yield identical aggregate overall
delay figures, as should be the case since the total amount of delay remains
unchanged between the two steps. However, they yield different average
aggregate origin and average aggregate destination delay figures due to the
different weights attributed to the origin and destination airports.
*
At the individual airport level, average overall delay results are different for Step
Al and Step A2. It is interesting to note that in all years, airports with delays
greater than average under Step Al (5.5 min/op in 1995, 6.6 min/op in 1997, and
8.4 min/op in 2000) were assigned even higher delays in Step A2. Similarly,
airports with delays smaller than average in Step Al were assigned even smaller
delays in Step A2. Therefore Step A2 resulted in an increase in spread among
69
delays experienced at different airports. This is illustrated in Figure 4.21, for year
2000.
COMPARISON STEP Al / STEP A2
0
73
0
COJ
0 0.
E
0n
0
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
W
W
SE STEP Al
0
C
N STEP A2
I
-~JOCa
0o
o-
=
Fiyure 4.2: Comparison of Step Al and Step A2 results for 2000
In 2000, the spread has more than doubled from 4.2 minutes per operation in Step Al to
8.8 minutes per operation in Step A2. The magnitude of the increase or decrease in
average delay from Step Al to Step A2 does not depend solely on the delay results
obtained in Step Al. It also depends on the relative congestion level of the airports that
are connected to the airport under consideration. For example, FLL and DTW had very
similar delays as computed in Step Al. However, in Step A2, the delays at FLL
decreased by over 1 minute while the delays at DTW barely decreased. This can be
explained by the fact that FLL is less congested than most of the airports it is connected
to. DTW, on the other hand, is connected for the most part with airports that operate at
similar congestion levels.
In the rest of the Chapter, we will only be referring to the results of Step A2 under
Method A.
18
Note that the same phenomenon can be observed for 1995 and 1997.
70
4.1.2
Method B
4.1.2.1
Step BI
Method B, unlike Method A, is based on the decomposition of gate-to-gate time into its
three components: taxi out, airborne, and taxi in times. The initial assumption (Step B1)
for Method B is that taxi out delay, taxi in delay, and airborne delay can be computed
independently and are completely uncorrelated.
In Step BI it is assumed that:
.
Taxi out delay is a result of congestion at the airport of origin and can therefore be
attributed to the airport of origin.
.
Taxi in delay is a result of congestion at the destination airport and can therefore be
attributed to the destination airport.
.
Airborne delay is a result of congestion at the destination airport and can therefore be
attributed to the destination airport.
The cause of airborne delay is usually not as clear as that of taxi out or taxi in delay.
Airborne delay can be caused by airspace congestion unrelated to any airport or can be
due to an airport other than the origin or destination airport of a specific flight. It can
also be caused by congestion at the destination airport, which results in the aircraft being
held airborne for a longer period of time. In Step B 1, we will assume that airborne delay
is fully attributable to the destination airport.
The gate-to-gate time for each flight is thus decomposed into three segments: taxi-out,
airborne and taxi-in. The baseline for each of the three O-D segments (BTOQ5 , BTIjj,
BAIRA5 ) is then calculated using the fifteenth percentile method (similar to that used for
the calculation of the gate-to-gate baseline time in Chapter 3).
Taxi out, taxi in and airborne delays (DTOh5 , DTI.5 , DAIRf ) are calculated for each 0D pair. Taxi out delay is taken as the difference between the average actual taxi out time
and the taxi out baseline calculated as described above:
71
1 ..............................................................
D T O|,5= A TOu;(y) - B TOQ
(4.11)
Similarly, taxi in and airborne delays are calculated as the difference between the average
actual taxi in (airborne) time and the taxi in (airborne) baseline:
DTIA TI (y) -BTI15
D sT~ A T
i(
(4.12)......
) -B T ls.. . . .. . . . ................................................(4.1 2)
..........
......
..
DAIR j - AAIRi, (y) -BAIR
............................... (4.13)
Average origin delay at a given airport a is taken to be the weighted average of taxi out
delays at that airport:
OrgAD3,(y)= (
DTO" (y) * TF, (y)) /
Z
TFaj(iy) .................................
(4.14)
Average destination delay at a given airport a is taken to be the weighted average of taxiin and airborne delays at that airport:
Des1AD3a(y)= (Z(DTI5 (y)+ DAIR 5 (y)) *TFi(y))Y
i
TFia (y) ............... (4.15)
i
Average overall delay at airport a is then taken to be the weighted average of origin and
destination delay at airport a (4.16).
Aa 3(y) = OrgAD3 (y)*
[Z TF j (y)+
(Z TF,
(y)) +
DestAD3, (y)*
(Z TF ,(y))]
TF (y)) ].................................................................(4.16)
Additional details can be found in Appendix C.
Table 4.3 shows airport delays in 1995, 1997, and 2000, computed according to Step B 1.
72
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
DFW
DTW
EWR
FLL
IAD
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
PHX
PIT
SFO
TPA
METHOD B (step 1)
AIRPORT DELAYS 2000
AIRPORT DELAYS 1997
AIRPORT DELAYS 1995
' UL I J ".L
IU
DEST97 ALL97
ORGO0
DET00
ALLUU
ORG95 IDEST95 IALL95
0RG97
11.8
13.2
10.4
10.6
13.9
7.4
9.6
11.3
7.9
13.1
15.7
10.4
9.2
12.1
6.3
7.6
9.9
5.2
7.9
9.4
6.3
5.7
7.9
3.6
6.1
8.1
4.1
9.8
10.2
9.4
8.1
9.7
6.5
6.4
8.1
4.7
8.9
9.8
8.1
7.8
10.2
5.3
6.9
8.6
5.1
6.7
8.0
5.4
6.1
8.0
4.2
5.0
6.6
3.4
10.0
10.5
9.5
8.3
9.9
6.6
6.3
7.2
5.3
8.5
8.8
8.1
7.1
8.5
5.8
6.4
7.7
5.1
10.1
13.8
6.5
8.8
11.6
5.9
8.5
11.7
5.4
11.0
13.4
8.6
12.2
15.7
8.8
11.5
14.9
8.0
11.9
12.8
10.9
10.1
11.9
8.3
9.6
11.7
7.5
15.0
14.6
15.5
13.4
14.0
12.8
10.0
10.8
9.2
8.9
11.3
6.8
7.0
10.7
3.7
6.7
10.0
3.8
11.7
13.8
9.7
7.7
10.4
5.0
6.1
7.9
4.3
10.7
12.6
8.8
9.5
12.5
6.6
8.9
12.3
5.5
11.1
14.8
7.4
9.8
13.5
6.2
9.5
13.3
5.8
14.0
12.5
15.5
10.2
10.6
9.9
8.3
9.0
7.7
7.8
10.0
5.5
7.2
10.7
3.7
7.1
10.1
4.0
7.5
9.1
5.8
7.9
9.7
6.0
6.4
8.4
4.3
10.2
12.3
8.1
10.5
13.4
7.5
10.6
13.1
8.1
12.2
14.6
9.9
10.4
13.1
7.8
8.7
10.9
6.5
12.4
15.1
9.6
9.6
12.4
6.8
8.5
10.8
6.0
14.2
14.5
14.0
9.6
11.8
7.5
6.6
8.3
4.9
9.7
12.6
6.7
7.6
10.2
5.1
6.7
9.5
4.0
8.2
9.2
7.3
6.6
8.8
4.5
6.5
8.1
4.8
12.3
16.7
7.9
10.0
12.7
7.3
9.9
13.5
6.3
7.2
9.1
5.2
7.2
9.8
4.3
6.5
9.3
3.4
8
83
A69
11
9.2
11.0
106
9.4
.)c
.nr
.
12.8
60.
Table 4.3: Average airport delays (min/op) obtained using Step BI
The airport with the highest delays in 2000 incurred 15 minutes of delay per operation.
Similarly the airport with the least delays in 2000 incurred 6.7 minutes of delay per
operation. The spread between the highest overall delay incurred and lowest overall delay
is therefore rather large (about 8.3 minutes).
In comparison to the results obtained in Steps Al and A2, Step B1 delay results are
significantly higher. This could be an indicator of potential correlation between taxi out,
taxi in, and airborne times, which needs to be adjusted for.
73
4.1.2.2
Step B2
Step B2 of Method B corrects for the potential correlation between taxi out, taxi in, and
airborne times by applying a factor of correction to the delay figures calculated in Step
Bi.
The taxi out, taxi in, and airborne delays obtained from Step B 1 are multiplied by a
correction factor CORKi, specific to each O-D pair. This correction factor is taken to be
equal to the ratio of the sum of the taxi out, taxi in, and airborne baselines divided by the
gate-to-gate baseline time, as shown in (4.17).
.. ....... ..... ...... .........
CORRU (y) = (BTO" + BTI" + BAIR
)/ B ..
Note that (BTO" + BTI 5 + BAIR," )
B, 5 . This is due to the fact that when taxi out, taxi
(4.17)
in, and airborne times are treated independently, we are looking at the best performance
on each individual segment. For example, the smallest taxi out times might be associated
with a particular runway configuration, which might generate the best taxi out times but
might not generate the best airborne time.
Origin delay is computed by averaging the adjusted departure delays:
OrgAD4,(y)=
(
CORRj (y) * DTO" (y) * TF/ (y))) /
TFj (y) ..................... (4.18)
8
jj
Similarly, destination delay is computed by averaging the adjusted arrival delays.
DestAD4a(y) =(
CORRi,(y)* (DTI|"(y)+ DAIR" (y)) * TF (y))/
ia
TF,(y) ..(4.19)
i
Average overall delay is then taken to be the weighted average of origin and destination
delay at airport a:
Aa4(y) =OrgAD4,(y)*
(ZTF (y)) +
.1
DestAD4,(y)*
(ZTF,(y))]
/
(
[Z(TF,1 (y )+ZTF1 (y )) ]...................................................(4.20)
74
Airport delays in 1995, 1997, and 2000 were computed using Step B2 as shown in Table
4.4.
AIRPORT DELAYS 1995
ORG95
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
DFW
DTW
EWR
FLL
IAD
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
PHX
PIT
SFO
TPA
7.5
5.0
3.9
4.5
4.9
3.2
5.0
4.8
5.2
7.7
7.1
8.6
3.7
4.2
5.3
5.6
7.2
3.9
4.1
7.7
6.2
5.7
4.7
3.9
4.5
6.0
3.3
5.7
_
DEST95 ALL95
10.7
9.1
9.4
7.2
7.7
5.8
7.7
6.1
8.2
6.5
6.3
4.8
6.9
6.0
7.3
6.0
11.2
8.2
14.1
10.9
11.0
9.0
10.3
9.5
9.5
6.5
7.6
5.9
11.7
8.5
12.7
9.1
8.6
7.9
9.6
6.8
8.0
6.1
12.5
10.1
10.4
8.3
10.3
8.1
7.9
6.3
9.1
6.5
7.7
6.1
13.0
9.5
8.8
6.2
10.1
7.9
METHODB (step 2)
AIRPORT DELAYS 1997
AIRPORT DELAYS 2000
ORG97 DEST97 ALL97
ORGOO
DESTOO ALLOO
7.0
13.2
10.1
9.8
12.5
11.2
6.0
11.5
8.7
10.0
15.0
12.5
3.4
7.5
5.5
6.0
9.0
7.5
6.2
9.2
7.7
8.9
9.7
9.3
5.1
9.7
7.4
7.7
9.4
8.5
4.0
7.6
5.8
5.1
7.6
6.3
6.3
9.5
7.9
9.0
10.1
9.5
5.5
8.0
6.8
7.6
8.4
8.0
5.7
11.1
8.4
6.2
13.2
9.7
8.4
14.9
11.6
8.2
12.7
10.4
7.8
11.2
9.5
10.3
12.1
11.2
12.1
13.3
12.7
14.6
14.0
14.3
3.5
10.2
6.7
6.6
10.9
8.6
4.8
10.0
7.4
9.3
13.3
11.3
6.3
11.9
9.1
8.5
12.0
10.2
6.0
12.9
9.4
7.1
14.2
10.7
9.3
10.1
9.7
14.6
12.0
13.3
3.5
10.2
6.9
5.3
9.6
7.5
5.7
9.3
7.5
5.5
8.7
7.1
7.2
12.8
10.0
7.8
11.7
9.8
7.4
12.6
9.9
9.4
13.9
11.6
6.5
11.8
9.2
9.2
14.4
11.8
7.1
11.3
9.2
13.3
13.8
13.6
4.9
9.7
7.3
6.5
12.1
9.3
4.3
8.4
6.3
7.0
8.8
7.8
7.0
12.2
9.6
7.6
16.2
11.9
4.1
9.4
6.9
5.0
8.7
6.9
6.51
12.2
11.3
10.5
8.9
8.81
Table 4.4: Average airport delays (min/op) obtained using Step B2
The following observations can be made when comparing the results of Step B 1 and Step
B2:
"
Step B2 yields smaller delay figures for all airports. Reductions in average overall
delays resulting from the adjustment for potential correlation range from 3.6% to
5.8%, depending on the individual airport. The average reduction is of the order
of 4.8%.
" The spread between average delay incurred by the airport with the most (EWR)
and the least delay (CMH) remains relatively stable from Step B1 (8.3 minutes
per operation) to Step B2 (8.0 minutes per operation), in 2000.
75
AIRPORT DELAYS 1995
DEST95
ALL95
ORG95
Step A2
5.5
5.6
5.5
AIRPORT DELAYS 1997
DEST97
ALL97
ORG97
5.5
7.7
6.6
AIRPORT DELAYS 2000
ORGOO
DESTOO
ALLOO
8.4
8.4
8.4
$
Step B2
5.7
10.1
7.9
6.5
11.3
8.9
8.8
12.2
10.5
Table 4.5: Comparison at the aggregate level of airport delays obtained using Step A2
and Step B2
At the aggregate level" (Table 4.5), the difference in average overall delay between Step
A2 and Step B2, in each year, is consistent. It ranges from 2.1 to 2.4 minutes per
operation. This discrepancy seems to arise from the fact that destination delay calculated
using Step B2 is significantly higher than that calculated using Step A2. Note that Steps
A2 and B2 are not expected to yield the same overall aggregate delay figures because
they are based on two fundamentally different methods. Method A is an iterative method
based on the attribution of a variable portion of the overall O-D delay to the airports of
origin and destination, depending on the relative congestion at those airports. Method B
is based on the decomposition of gate-to-gate time into its three components (taxi out
time, airborne time, taxi in time), the calculation of individual component delays, and the
attribution of entire component delays to the relevant airport (taxi out delay to the origin
airport, taxi in and airborne delay to the destination airport).
At the individual airport level:
" Step B2 always yields higher destination and higher overall average delay, in all
years, for all individual airports. However, it does not always yield higher origin
delays.
*
In Step B2, destination delay is higher than origin delay in all years, except for
LGA and EWR in 2000. Results obtained using Step A2, however, do not show a
systematically higher destination delay.
At the aggregate level, we can consider the average delay per airport, obtained as a weighted
average of
the delays incurred by the 27 individual airports.
19
76
Although origin delays in Step A2 and B2 are comparable at the individual or aggregate
level, it is evident that even after adjustments for potential correlation, destination delays
in Step B2 are significantly higher than those obtained in Step A2. Step B2's systematic
overestimation of destination delays suggests that the assumption that airborne delays are
fully attributable to the destination airport may be invalid.
4.1.2.3
Step B3
Step B3 does not use the assumption that airborne delay is fully attributable to the
destination airport. Instead, airborne delay is assumed to be due exclusively to airspace
congestion unrelated to any specific origin-destination airport pair. In this respect, it
should not be attributed to any airport.
Taxi-out and taxi-in delays are then calculated as in Step B 1.
Average origin delay at airport a is also calculated as in Step B 1:
OrgAD5,(y) = OrgAD3,(y) ...............................................................
(4.21)
Average destination delay at airport a is taken to be the weighted average of taxi-in
delays at that airport:
DestAD5( (y) =
(Z(DTI1
(y))* TFia (jy))/................................(4.22)
i
Average overall delay is then taken to be the weighted average of origin and destination
delay at the airport a:
Aa 5(y) =OrgAD5, (y)*
[Z TF,(y)+
(ZTFI (y)) +
DestAD5, (y)*
/
(ZTF, (y))]
TF,(y)) ] ...................................................................
(4.23)
Table 4.6 shows airport delays in 1995, 1997, and 2000, computed according to Step B3.
77
AIRPORT DELAYS 1995
ORG95
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
DFW
DTW
EWR
FLL
lAD
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
PHX
PIT
SFO
TPA
7.9
5.2
4.1
4.7
5.1
3.4
5.3
5.1
5.4
8.0
7.5
9.2
3.8
4.3
5.5
5.8
7.7
4.0
4.3
8.1
6.5
6.0
4.9
4.0
4.8
6.3
3.4
6.0
M ETHO D B (Step B 3)
AIRPORT DELAYS 1997
__
IDEST95 |ALL95
ORG97 IDEST97 JALL197
2.4
5.2
7.4
2.8
5.1
2.4
3.8
6.3
2.7
4.5
1.7
2.9
3.6
1.8
2.7
2.0
3.4
6.5
1.6
4.1
2.2
3.7
5.3
2.2
3.8
1.4
2.4
4.2
1.7
3.0
1.5
3.4
6.6
1.8
4.2
2.5
3.8
5.8
2.7
4.2
2.9
4.2
5.9
2.9
4.4
4.6
6.3
8.8
5.6
7.2
4.2
5.9
8.3
4.7
6.5
2.6
5.9
12.8
3.0
7.9
1.3
2.6
3.7
1.4
2.6
1.6
3.0
5.0
1.8
3.4
2.6
4.0
6.6
2.5
4.5
3.8
4.8
6.2
4.2
5.2
2.3
5.0
9.9
2.9
6.4
2.2
3.1
3.7
1.7
2.7
1.6
3.0
6.0
2.2
4.1
3.1
5.6
7.5
3.5
5.5
2.2
4.4
7.8
2.8
5.4
3.2
4.6
6.8
3.5
5.2
1.9
3.5
7.5
2.7
5.2
1.5
2.8
5.1
2.1
3.6
2.0
3.4
4.5
1.8
3.1
2.1
4.2
7.3
2.3
4.8
1.4
2.4
4.3
1.8
3.0
2.6 ,
4.3
2.91
4.9
6.91
,6,,4
__AIR
PO RT
_D
ELA
YS
_200
AIRPORTDELAYS2000
ORGO0
I
DESTOO ALLOO
10.4
3.9
7.1
10.4
4.2
7.3
6.3
2.3
4.3
9.4
1.6
5.4
8.1
2.5
5.3
5.4
1.8
3.6
9.5
2.3
5.9
8.1
1.9
4.9
6.5
3.9
5.2
8.6
4.9
6.8
10.9
5.1
8.0
15.5
4.2
9.8
6.8
2.2
4.7
9.7
2.7
6.2
8.8
2.8
5.9
7.4
4.7
6.1
15.5
4.0
9.7
5.5
2.1
3.8
5.8
2.1
4.0
8.1
3.5
5.8
9.9
3.2
6.6
9.6
4.9
7.2
14.0
4.0
8.9
6.7
3.1
5.0
7.3
2.4
5.0
7.9
2.6
5.3
5.2
2.0
3.5
9.2
3.5
6.4|
3.5
Table 4.6: Average airport delays (min/op) obtained using Step B3
Step B3 yields very small destination delay results. These destination results are much
smaller than those obtained through Method A (Step A2). They are on the order of half
the destination delays obtained in Step A2. This observation suggests that the assumption
that airborne delays are exclusively caused by airspace congestion is not valid, either. In
fact, it seems that some portion of the airborne delays should indeed be attributed to the
destination airport.
4.1.2.4
Step B4
In view of the results obtained in Step B 1, Step B2 and Step B3, it is reasonable to
assume that neither one of the hypotheses used in Steps B1, B2 and B3 regarding the
allocation of airborne delays is well-founded. In fact, it would be more reasonable to
78
assume that a portion of the airborne delay is due to the destination airport and the
remaining portion is due to airspace congestion. In Step B4, we will assume that a
fraction p of the airborne delay is due to the destination airport, while the remainder is
due to airspace congestion. The magnitude of airport delays will depend on the fraction p
chosen. We will choose p such that the differences between average overall delay results
obtained using Step A2 and Step B4 are minimized.
This problem is equivalent to:
Min I (A2(95) - AZ6(95))2 +
M a{ (a 2(5 Aa(5)
(A,2(97) - A, 6(97))2
a
+1
(A 2(00) - A, 6(00))2
where
TFj (y) .................................
OrgAD6a(y, p) = (ZDTO" (y) * TFj (y))/
DestAD6, (y, p) = (
(DTI (y) + P * DAIR5 (y))* TFi (y))/ (
(4.24)
TF (y) ........... (4.25)
ii
A(J6(y, p) = rOrgAD6, (y, p)
*
(ZTF ( y)) +
DestAD6a (y, p) *
I
[
TF (Y )+Z
TFia(Y )) I......................................................
(ZyTF(y))]
/
i
............ (4.26)
Figure 4.3 illustrates the effect of the choice of p on the aggregate average overall delay.
The aggregate average overall delay increases by about 4 to 5 minutes per operation
when using p=I rather than p=0. This shows that the choice of p has a very significant
impact.
79
Figure 4.3: Sensitivity of aggregate overall delay results to fraction p chosen
The objective function is minimized for p=0.4 . The corresponding delay results are
shown in Table 4.7.
80
J
METHODB (Step
B4)
AIRPORT DELAYS 2000
AIRPORT DELAYS 1995
AIRPORT DELAYS 1997
DESTOO IALLOO
ORG95 DEST95 ALL95
ORG97
ORGOO
DEST97 ALL97
9.0
7.4
7.2
7.3
10.4
7.6
7.9
5.9
6.9
5.2
5.4
5.3
6.3
6.4
6.3
10.4
8.8
9.6
4.1
4.2
4.2
3.6
4.2
3.9
6.3
5.2
5.7
7.2
5.0
6.5
4.8
5.7
9.4
4.6
4.7
4.4
8.1
5.4
6.7
5.4
5.1
4.8
4.9
5.3
5.4
4.2
4.8
4.2
4.2
5.4
3.5
3.4
4.2
3.4
9.5
5.6
7.5
4.6
6.6
5.1
5.8
3.8
5.3
5.1
4.6
4.8
5.8
5.0
5.4
8.1
4.7
6.3
6.3
6.1
6.5
7.8
7.1
5.4
6.4
5.9
5.9
8.4
9.6
9.2
8.6
8.3
8.0
8.7
8.4
8.8
ATL
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
DFW
DTW
EWR
7.5
9.2
7.1
5.8
7.3
7.5
8.3
12.8
7.6
7.3
7.9
10.1
10.9
15.5
8.1
8.3
9.5
11.9
FLL
4.7
4.1
4.3
4.2
3.7
5.0
5.1
5.2
4.3
5.1
6.8
9.7
5.8
7.1
6.4
8.4
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
3.8
4.3
5.5
5.8
7.7
4.0
4.3
8.1
6.5
6.0
4.9
6.4
6.0
6.6
6.5
6.5
8.8
6.7
7.8
7.6
5.0
5.3
4.3
7.1
5.6
6.2
4.5
6.7
6.3
4.7
4.3
7.6
6.1
6.1
4.7
6.2
9.9
3.7
6.0
7.5
7.8
6.8
7.5
7.0
7.9
4.5
5.6
7.5
7.4
6.9
6.9
7.4
15.5
5.5
5.8
8.1
9.9
9.6
14.0
8.7
7.4
5.2
4.9
7.0
7.7
8.9
8.1
8.1
11.4
5.4
5.4
7.6
8.8
9.3
11.1
PHX
4.0
4.7
4.3
5.1
5.2
6.7
6.9
6.8
PIT
SFO
TPA
4.8
6.3
3.4
6.0
4.4
6.6
4.5
5.8
4.6
6.4
4.0
5.91
4.5
7.3
4.3
6.9
7.9
6.0
5.3
5.2
7.4
6.9
7.0
6.3
5.3
4.6
6.4
5.0
6.51
4.5
6.8
4.7
6.7
7.3
7.9
5.2
9.2
5.1
8.2
4.8
7.21
6.3
8.1
5.0
8.2
IAD
Table 4.7: Average airport delays (min/op) obtained using Step B4
Results obtained using Step B4 are consistent with those obtained in Step A2. A detailed
comparative analysis between the two sets of results is described in the next section.
4.2
Analysis and Interpretation of Results
4.2.1
Comparative Analysis
First, at the aggregate level, we can consider the aggregate average overall delay per
airport, obtained as a weighted average of the delays incurred at the 27 individual
airports.
81
...........
.
AIRPORT DELAYS 1995
4
AIRPORT DELAYS 1997
AIRPORT DELAYS 2000
ORG95
DEST95
ALL95
ORG97
DEST97
ALL97
ORGOO
DEST0O
ALLOO
Step A2
5.5
5.6
5.5
5.5
7.7
6.6
8.4
8.4
8.4
Step B4
6.0
5.8
5.9
6.9
6.5
6.7
9.2
7.2
8.2
Table 4.8: Comparison at the aggregate level of airport delays (min/op) obtained using
Step A2 and Step B4
At the aggregate level (Table 4.8), the following observations can be made:
" Both methods show an increase in the aggregate average overall delay per airport
from 1995 to 2000. This increase is of about 53% (for Step A2) and 39% (for Step
B2) between 1995 and 2000.
" Aggregate average destination delay is greater than or equal to origin delay for
Step A2. Aggregate average destination delay is smaller than average origin delay
for Step B4.
Figure 4.4: Airport delays in 2000 calculated as a function of the methodology
82
At the individual airport level (Figure 4.4), some of the observations made at the
aggregate level no longer hold. Specifically,
" Both methods show increases in the average overall delay from 1995 to 2000, at
the individual airports. The only exception is MIA20
*
There does not seem to be any trend concerning a systematically higher origin or
destination delay for either method.
*
Airport delays in 2000 range from 4.5 minutes per operation to 13.3 minutes per
operation depending on the airport under consideration and the method used to
estimate the delay.
Spread (min/op)
ORG95
DEST95
ALL95
ORG97
DEST97
ALL97
ORGOO
DESTOO
ALLOO
10.2
8.5
8.8
10.3
4.7
7.1
Step A2
5.2
5.7
4.3
8.0
6.2
7.1
Step B4
5.8
5.2
4.9
9.2
5.4
6.2
Table 4.9: Comparison of spreads for Step A2 and Step B4
Table 4.9 shows that the gap between average delay incurred by the airport with the most
and the least delay has increased over the 1995-2000 period, for both methods. For Step
A2, the gap has increased from 4.3 to 8.8 minutes per operation, which represents a 105%
increase; for Step B4, the gap has increased from 4.9 to 7.1 minutes per operation (45%
increase). This shows that over the years, delays have increased significantly more at
certain airports than at others. This is due to the fact that delays increase non-linearly
when airports operate near their capacity. Airports operating near capacity in 1995 saw
their delays increasing at a faster rate than the airports that were not operating near
capacity. It is also interesting to note that the greater increase in spread occurs for the
origin delay, for both methods.
Average delay at MIA airport decreased by 0.2 minutes per operation from 1995 to 2000,when calculated
using Step A2. This can be explained by the fact that traffic growth in MIA was very slow over the years.
20
83
4.2.2
Standard Deviations
In addition to providing an estimation of airport delays, Method B yields interesting
insights as to the validity of the assumptions it is based on.
Standard deviations of taxi out delays were computed for the airport of origin (4.27) and
airport of destination (4.28) for the years 1995, 1997, and 2000.
SDORG(TO,y) =
( D TO" (y) ).....................................................(4.27)
SDaDEST(TO,y) =a
( D TO, (y) )....................................................(4.28)
Standard deviations of taxi-in delays were computed for the airport of origin (4.29) and
airport of destination (4.30) for the years 1995, 1997, and 2000.
SD2RG(TI,y)
= - ( D TI " (y) ).......................................................(4.29)
SD)EST(TI,y) =
(D TI, 5 (y) )...............................................
. (4.30)
Standard deviations of airborne delays were computed for the airport of origin (4.31) and
airport of destination (4.32) for the years 1995, 1997, and 2000.
SD2RG(AIR,y)=-a ( DAIRg (y) )....................................................(4.31)
SDEST(AIR,y)
(DAIR(y)
)..
......................................
(4.32)
Methodology and detailed results are shown in Appendix D.
Step B I results show that taxi out delays at a specific origin airport tend to be similar on
average, regardless of the destination. This is indicated by the small standard deviations
(SDa)RG(TO,y))
shown in Figure 4.5.
84
STD.DEV TAXI OUT DELAY (2000)
4.5 4
35
3
0
_______________
_________
.-.
__________
-
5
i
0.
50
<
0t0 <
XX
2 CL
2W 0X CL
jLM CLU-U) L
-
ODODO3:W
SESDORG(TO,2000)
MSD
DEST (TO, 2000)
Figure 4.5: Standard deviation of taxi out delays grouped by origin airport vs. destination
airport
Figure 4.5 shows that the standard deviation for taxi out delay for all O-D pairs
originating at a given airport a - SD ORG (TO,2000)-is much smaller than the standard
deviation of the taxi out delays for all O-D pairs arriving at that airport,
SDDEST (TO,2000). The same observation can be made for the years 1995 and 1997.
The values of the standard deviations of taxi out delays SDRG (TO, y) are very small in
magnitude. They are mostly in the 0.7-1.5 minutes range, in all years. The coefficients of
variation for taxi out delays grouped by origin airport in 2000 range from 0.12 to 0.25,
which indicates a tight distribution of taxi out delays at each origin airport. This shows
that there is a strong correlation between taxi out delay and airport of origin and justifies
the decision to attribute taxi out delay to the origin airport.
85
Figure 4.6: Standard deviation of taxi in delays grouped by origin airport vs. destination
airport
The standard deviations of taxi in delays occurring on O-D pairs terminating at airport a SDEST (TI,2000) - are much smaller on average
21
than the standard deviations of taxi in
delays occurring on O-D pairs originating at airport a, SDORG(TI,2000), as shown by
Figure 4.6. The values of SDDEST (TI,2000) are very small, with most of them in the 0.20.7 minute range, in all years. The coefficients of variation of taxi in delays grouped by
destination airports in 2000 range from 0.10 to 0.31; this shows a strong correlation
between taxi in delay and destination airport and justifies the decision to attribute taxi in
to the destination airport.
21
Except for DTW
86
Figure 4.7: Standard deviation of airborne delays grouped by origin airport vs. destination
airport
The standard deviations of airborne delays occurring on O-D pairs with the same
destination airport (SDEST(AIR,y)) are slightly smaller, but comparable in magnitude, to
the standard deviations of airborne delays occurring on O-D pairs originating at the same
airport (SDYRG(AIR,y)), as shown in Figure 4.7. The coefficients of variation of airborne
delays grouped by destination airports in 2000 range from 0.19 to 0.43; these suggest that
airborne delays are not that strongly correlated with the destination airport. This confirms
our previous hypothesis that airspace congestion, which cannot be attributed to any
specific airport, might be at least partly responsible for the airborne delays. This also
explains why destination delay results in Step B 1 and B2 were so high. It also suggests
that Step B4 is the most appropriate approach, in Method B, to estimate airport delays.
87
In this chapter, we described two methodologies that could be used to attribute the O-D
delays calculated in Chapter 3 to the origin and destination airports. Both methods
yielded delay results that showed a significant increase in the average delay from 1995 to
2000, at each of the 27 airports considered.
88
CHAPTER 5: APPLICATIONS
In Chapter 4, two methodologies were used to estimate the average origin, destination,
and overall delay per operation at each of the 27 airports under consideration. Chapter 5
illustrates two applications of the results obtained in Chapter 4. Section 5.1 describes the
calculation of total annual delays at Logan airport. Section 5.2 compares airport rankings
derived from Chapter 4 with airport rankings published in the 2001 airport capacity
benchmark report.
5.1
Lo2an Airport Annual Delays
5.1.1
Calculations
Logan International Airport (BOS) is the world's
3 2 nd
busiest airport in terms of
passenger volume. It is serviced by over 55 scheduled airlines (of which 8 are major
domestic carriers, 16 are non-US flag carriers, and 13 are regional and commuter
airlines) . Operations also include general aviation flights.
22
Source: Massport website
89
In Chapter 4, the following results were obtained for Logan airport.
ORG95
FLIGHTS (SAMPLE)
25,882
AVERAGE DELAY USING
5.7
STEP A2_(minlop)
IDEST95
25,933
5.5
ALL95
51,815
AIRPORT BOS
IDEST97
ALL97
ORG97
28,004
28,105
ORGOO
5.2
5.4
ALLOO
56,109
22,112
22,107
44,219
5.6
7.8
7.4
7.6
11.6
12.8
12.2
5.3
6.3
6.4
6.3
10.4
8.8
9.6
____________________________
AVERAGE DELAY USING
STEP B4 (minlop)
DESTOO
Table 5.1: BOS airport delays -
Table 5.2 shows the number of total annual operations (OP(y)) at BOS airport.
1995
Annual
476,846
OperationsII
Airport BOS
1997
2000
502,187
508,283
Table 5.2: Total number of operations at BOS airport (Source: CODAS database)
Table 5.2 shows that the total number of operations at Logan airport increased by 6.6%
over the 1995-2000 period. Using the total number of operations per year, and assuming
an equal number of departures and arrivals, total annual delay at BOS airport can be
computed. Annual delays were calculated based on the results of Step A2 and Step B4, as
shown in equations (5.1) and (5.2).
YD2BOS (y)= [ OrgAD2,(y) * OP(y) / 2 + DestAD2a(y)* OP(y) / 2 ] /60 ......... (5.1)
YD6 BOS(y)= [ OrgAD6(,(y) * OP(y) / 2 + DestAD6,(y) * OP(y) / 2 ] /60...........(5.2)
The table below shows the sensitivity of the total annual delay at Logan to the
methodology used:
Note that the numbers reported in the "FLIGHTS" row of the table indicate the number of scheduled jet
flights flown by the 10 major carriers in the months of January, April, July, and October for 1995 and 1997,
and January, April, and July for 2000. These only represent a small sample (roughly 8-11% depending on
the year) of the total number of flown flights during these years.
23
90
AIRPORT BOS
TOTAL
DEST
ORG
TOTAL
DEST
ORG
97
DELAY
97
DELAY
97
DELAY
95
DELAY
95
DELAY
DELAY 95
ORG
DELAY
DEST
DELAY
TOTAL
DELAY
TOTAL ANNUAL
DELAYS BOS USING
STEP A2 (hrs/year)
22,750
21,952
44,702
32,788
30,803
63,590
49,017
54,191
103,208
TOTAL ANNUAL
DELAYS BOS USING
STEP B4 (hrslyear)
20,768
21,433
42,201
26,205
26,928
53,133
44,230
37,196
81,426
Table 5.3 Total Annual Delay at Logan airport
Table 5.3 indicates that our best estimate of the annual aircraft delay hours incurred at
Logan in 2000 is in the range of 80,000 - 105,000. The delay estimates we obtain from
our two methods fall within 6% of each other in 1995, 16% in 1997, and 21% in 2000.
Both estimates also show that annual delays at BOS almost doubled from 1995 to 2000.
Analogous estimates to those shown in Table 5.3 can easily be obtained for the other 26
airports in our sample.
5.1.2 Discussion of Results
The delay estimates obtained in Chapter 4 were based on data extracted from the ASQP
database. The ASQP database reports information for the 10 major US airlines, and only
contains data for scheduled jet operations. However, ASQP carriers' scheduled jet
operations only represent about 40% of total annual operations at Logan Airport24
Therefore the average delay figures obtained in Chapter 4 are representative of only one
category of aircraft operations at Logan.
In order to obtain total annual delay results, we implicitly assumed that all flights,
whether general aviation or commercial aircraft flights, experience delays similar to those
Note that as of October 2002, the breakdown per operation type at Logan airport was as follows:
58% air carriers, 35% commuters, and 7% general aviation.
24
91
of jets flown by major carriers. The calculation above therefore represents an
approximation: it might not be accurate to extrapolate and infer that non-ASQP carriers
(in general smaller carriers) and general aviation would incur the same average delay. A
future direction of research could be to compute separately delays for regional carriers
and general aviation operations. However, data on such operations are hard to come by.
5.2
Airport rankings
Table 5.4 is an extract from the 2001 airport capacity benchmark report and shows the 31
most congested airports in the US. They are ranked according to the proportion of flights
delayed according to the FAA's Operations Network (OPSNET) database.
From take-off to landing, each flight travels through different sectors under the
supervision of different ATC facilities (en-route control centers, terminal radar approach
control, and airport control towers). In OPSNET, statistics are collected independently
by each ATC facility in charge of the sector the plane is flying through. A flight is
considered delayed in a specific sector or airport if its elapsed flight time in the sector
exceeds its flight plan time in the sector by more than 15 minutes. The OPSNET
reporting method results in the fact that a single aircraft might incur more than one
reportable delay as it progresses through the different sectors.2 5 Conversely, and this is a
more frequent situation, an aircraft might incur a cumulative delay of more than 15
minutes over the whole flight but might never be reported as being late if the individual
delays in each sector do not exceed 15 minutes. For this reason, OPSNET statistics
greatly underestimate the extent of true delays.
25
http://www.faa.gov/apa/janOI del.htm
92
Airport
ranked by
delay
LGA
EWR
ORD
SFO
BOS
PHL
JFK
ATL
IAH
DFW
PHX
LAX
IAD
STL
DTW
CVG
MSP
MIA
SEA
Delays per
1000
operations
155.0
81.2
63.3
56.8
47.5
44.5
38.8
30.9
28.1
23.8
22.0
21.9
19.5
18.2
17.6
15.4
12.7
11.3
10.4
LAS
8.0
DCA
BWI
MCO
CLT
PIT
SAN
DEN
SLC
TPA
MEM
HNL
8.0
6.9
6.3
6.0
3.8
2.5
2.2
2.0
1.6
0.4
0.0
Table 5.4: Airport rankings by proportion of flights delayed (OPSNET)
(Source: Airport Capacity Benchmark 2001)
Our analysis has focused on 24 of the airports listed in Table 5.4, namely: LGA, EWR,
ORD, SFO, BOS, PHL, ATL, IAH, DFW, PHX, LAX, IAD, DTW, CVG, MSP, MIA,
DCA, BWI, MCO, CLT, PIT, DEN, TPA, MEM. In addition to these, we also considered
CLE, CMH, and FLL, as they represent large passenger markets as well.
93
In order to perform a comparison of the airport rankings derived from Chapter 4 results
with those obtained from the 2001 benchmark report, we only considered the airports that
were common to both data sets: CLE, CMH, FLL in our set of 27 airports were not
considered; similarly, JFK, STL, SEA, LAS, SAN, SLC, HNL which are included in the
benchmark report were not included.
Airport rankings in 2000
OPSNET proportion
Method A (Step Method B (Step of delayed flights
A2)
B4)
(based on 2001
benchmark report)
ATL
BOS
BW
CLT
CVG
DCA
DEN
DFW
DTW
EWR
IAD
IAH
LAX
LGA
MCO
MEM
MIA
MSP
ORD
PHL
PHX
PIT
SFO
TPA
8
4
18
20
10
22
16
14
11
1
6
13
12
3
21
24
15
9
5
2
17
19
7
23
7
4
23
19
15
21
17
9
5
1
10
13
11
2
24
25
14
8
6
3
18
22
12
26
7
5
18
20
14
17
22
9
13
2
12
8
11
1
19
24
16
15
3
6
10
21
4
23
Table 5.5: Comparison of airport rankings using Step A2, B4, and OPSNET
delays
94
Using Step A2 and B4 results, airports were ranked in decreasing order, from the airport
that incurred the highest average overall delay in 2000 to the one that incurred the lowest,
as shown in Table 5.5.
We then used the Spearman Rank Correlation test to compare the rankings and test
whether they were comparable, using the equation below:
r
1- 6 * (d' + d2 + .......... + d 2) /(n * (n 2 - 1)) ......................................
(5.3)
Spearman Rank Correlation Coefficient
Step A2 &
Step B4 &
OPSNET
OPSNET
Step A2 & B4
rankng
ranking
0.92
0.87
0.83
Table 5.6: Correlation between airport rankings
The coefficients obtained (see Table 5.6) are close to 1, indicating a very high correlation
between the different rankings. Despite the severe underestimation of total delays by
OPSNET, airport rankings derived from OPSNET and those obtained using Step A2 and
Step B4 are very consistent.
We also compared airport rankings obtained using Step A2 and Step B4 to the following
airport rankings:
*
OPSNET number of delays: airports are ranked according to total number of
flights delayed in 2000. The airport with the greatest number of delayed flights gets
the lowest rank.
0
ASPM average arrival delay: the Aviation System Performance Metrics
(ASPM)26 system reports arrival delays measured as the actual gate arrival time
minus the scheduled gate arrival time. This measure is equivalent to what we
referred to as "delays relative to schedule". Airports are ranked according to the
ASPM is the successor of the Consolidated Operations and Delay Analysis System
(CODAS) and is operated by the FAA Office of Aviation Policy and Plans. ASPM uses data gathered by
Aeronautical Radio Inc. (ARINC) to compile several metrics that describe the traffic, prevailing conditions,
and performance (actual vs. scheduled individual flight times, airport efficiency) for the previous day.
26
95
average arrival delay in 2000: the airport with the highest average arrival delay gets
the lowest rank.
*
ASQP on-time arrivals: airports are ranked according to the percentage of on-time
flight arrivals in 2000. The airport with the lowest percentage of on-time flights gets
the lowest rank.
*
Enplaned passengers: airports are ranked according to the number of enplaned
passengers in 2000. The airport with the highest number of enplaned passengers in
2000 gets the lowest rank.
*
OPSNET Total Operations Rank: the airport with the highest number of annual
operations in 2000 gets the lowest rank.
0
Optimum Capacity/Total Operations: Airports are ranked according to the ratio of
optimum airport capacity divided by total operations in 2000. The airport with the
lowest ratio gets the lowest rank.
*
Reduced Capacity/Total Operations: Airports are ranked according to the ratio of
reduced airport capacity (in bad weather conditions) divided by total operations in
2000. The airport with the lowest ratio gets the lowest rank.
Optimum Capacities and Reduced Capacities are estimates of maximum number of
flights per hour an airport can handle under good weather conditions2 7 and adverse
weather conditions28 , respectively. These figures were obtained from Table I of the
2001 FAA benchmark report. Note that we used the lower end of the reported ranges.
Total Operations represent the OPSNET Total Operations reported in the benchmark
report.
27
28
Good weather conditions consist of periods of unlimited ceiling and visibility
Adverse weather conditions may include poor visibility, unfavorable winds, or heavy precipitation.
96
Airport
RANKINGS OBTAINED USING...
ASPM ASQP onOPSNET
OPNT
OPSNET ~~SM
Enplaned
time
proportion NumbE of Average
Pa.
ime
Aria
fdlydNumber
Praa
x
Deas
Arrival
of delayed
arrivals
Dly
Delays
fihs
Delay
______
flights
Method A Method B
(Se 3)(tp14
(Step B2) (Step B4)
OPSNET Optimum
Reduced
Ceduced
Cptu
Cap./Total Cap.ITota
p
p.
I Ops
Ops.
Otal
Total
p.
Ops.
________
8
6
7
5
4
6
9
3
7
8
1
14
1
10
4
11
23
18
20
14
20
19
23
20
15
19
15
21
17
9
5
20
14
17
22
9
13
17
14
18
22
8
12
24
15
18
7
17
20
24
23
16
5
6
19
17
20
23
6
3
7
15
14
22
7
3
6
17
15
9
23
18
16
18
19
9
24
12
17
ATL
BOS
8
4
7
4
BWI
18
CLT
CVG
DCA
DEN
DFW
DTW
20
10
22
16
14
11
EWR
1
1
2
3
5
11
10
16
10
5
IAD
IAH
LAX
LGA
MCO
6
13
12
3
21
10
13
11
2
24
12
8
11
1
19
13
11
9
1
19
11
19
8
1
13
18
21
1
9
14
22
11
4
15
13
13
11
4
19
21
13
12
2
3
22
16
14
3
2
21
MEM
MIA
MSP
24
15
9
25
14
8
24
16
15
24
16
15
22
10
23
17
15
12
24
12
5
20
9
8
21
14
7
22
11
13
ORD
5
6
3
2
4
4
2
2
5
PHL
PHX
PIT
SFO
TPA
2
17
19
7
23
3
18
22
12
26
6
10
21
4
23
7
10
21
5
23
6
12
21
2
16
10
3
22
2
13
16
9
18
8
21
12
5
17
18
24
6
1
19
8
24
7
10
1
20
4
23
Table 5.7: Airport delay rankings using different criteria (Source for columns 3-10:
2001 Airport Capacity Benchmark Report)
Table 5.7 shows the airport rankings obtained depending on different criteria. Airport
rankings were compared using the Spearman Rank Correlation test. Results are shown in
Figure 5.1 below. Note that the matrix is symmetric but only the above-diagonal part is
shown in Figure 5.1.
97
RANKS
Spearman's Rank
Correlation
Method A
(Stop B32)
Method B
(Stop 134)
OPSNET
proportion
of delayed
OPSNET
Number of
Delays
0.87
0.83
flights
Metho
0.92
(Step
14)
OBTAIN4ED USING...
ASQP on-
ASPM
OPSNET
Ops.
Optimum
Reduced
CapjTotal Cap.ITotal
Ops.
Ops
Average
Arrival
Delay
time
arrivals
Enplaned
Pax.
0.85
0.67
0.37
0.39
0.39
0.62
0.59
0.84
0.48
0.31
0.46
0.48
0.58
0.56
0.98
0.69
0.50
0.47
0.38
0.75
0.82
0.67
0.54
0.54
0.47
0.77
0.82
0.68
0.30
0.16
0.47
0.61
0.65
0.47
0.52
0.61
0.81
Total
OPSNET
proportion of
delayed fliahts
z
of Delay
r
U Deray
A0 anrivas
P
Z
Enplaned Pax.
0.41
0.41
OPSNET Total
5
0.33
Ops.
0.45___0.33
Optimum
Cap.Total Ops.
Reduced
Cap.ITotal Ops I____
0.89
Figure 5.1: Correlation of airport rankings using different criteria (Spearman Rank
Correlation Test)
It can be observed from Figure 5.1 that:
*
The airport rankings obtained using Step A2, Step B4, OPSNET proportion of
delayed flights, and OPSNET total number of delayed flights are all strongly correlated.
0
There seems to be a very weak relationship between ASQP on-time rank and Step A2
and B4 ranks. This suggests that on-time statistics are a poor indicator of the true
severity of airport delays at different airports.
*
The relationship between Step A2 and B4 rankings and ASPM average arrival delay
ranking is rather weak. This shows that delay relative to schedule is not a good estimator
of true delays.
0
It is interesting to note that the OPSNET total number of delayed flights ranking is
well correlated with the ratio of reduced capacity over total operations ranking. This
shows a relationship between the number of flights delayed and the reduction in capacity
due to poor weather at an airport.
The above observations suggest that ASQP on-time statistics and average delay relative
to schedule are poor indicators of the true extent of air traffic delays. The measures
98
yielding airport rankings closest to those derived from Chapter 4 results are OPSNET
proportion of delayed flights and OPSNET total number of delayed flights. This
observation is surprising since we pointed out at the beginning of the Chapter that
OPSNET delay statistics severely underestimate delays. This suggests that despite the
numerous possible criticisms, OPSNET statistics can be useful in determining the relative
state of congestion at the different airports.
Chapter 5 provided two applications of the results derived in Chapter 4. In Chapter 6, we
will discuss the complexities associated with making optimal scheduling decisions,
through the development of a simple probabilistic model.
99
100
CHAPTER 6: OPTIMAL SCHEDULING: A SIMPLE
CASE STUDY
We showed in the previous chapters that both true delays and delays relative to schedule
have been increasing over the past years. True delays are measured against a fixed
benchmark, which cannot be adjusted. In contrast, delays relative to schedule can be
reduced by adjusting schedules: airlines can schedule their flights and turn times to match
anticipated actual transit times as closely as possible, therefore minimizing the
probability of incurring delays relative to schedule.
In this Chapter, we change our perspective and try to show why it may be very difficult
for airlines to optimize their schedules so as to achieve high schedule compliance records.
This analysis also shows some of the interdependences in the schedule that make airline
scheduling so complex.
Section 6.1 introduces the example that will be used in the remainder of the Chapter.
Section 6.2 explores alternative objective functions aimed at minimizing the cost of
delays. Section 6.3 consists of a discussion of the results obtained for each objective
function.
101
6.1 Context
The following case will be analyzed in the remainder of the Chapter.
Assume an aircraft is scheduled to fly from A to B, then fly back from B to A, as shown
in Figure 6.1.
tBa,
A
B,a
tAI
tBc
B,d
A
Figure 6.1: Spatial and temporal description of flight nath
The probability density functions of actual transit times on O-D pairs (A,B) and (B,A)
can be obtained from ASQP data such as those used in Chapters 3 and 4. In this particular
case, we will assume for simplicity that the probability distributions are known, and are
uniform, as shown in Figure 6.2.
ftAB*
ftBAA
0.5.
1
'2
t
I
Sab
Se
Figure 6.2: Probability distribution functions of actual transit times between A and B 29
The problem consists in determining the optimal schedule of the aircraft, based on the
given probability distributions of transit times on (A,B).
Figure 6.2 assumes that transit times from B to A are larger on average than transit times from A to B.
This is a common phenomenon, especially on medium-haul to long-haul flights. It is usually due to the
directionality of dominant winds.
29
102
The decision variables are:
scheduled transit time from A to B
*
Sub:
"
S9: scheduled turnaround time at B
SSba : scheduled transit time from B to A
The constraints are:
*
S9 > 0.5: the minimum turn time is assumed to be 0.5 hours.
0
1 Sab < 2
9 1
Sba
3
The objective function can take various forms depending on the goals to be achieved and
will be examined in more detail in Section 6.2.
Delays
6.1.1
6.1.1.1 Arrival Delay at B
Given the assumption of a uniform actual transit time between A and B, Figure 6.3
illustrates the probability distribution of arrival delay at B, as a function of Sab
P(delay-O)= Sab-1
11
0
2- Sah
arrival delay at B (min)
Figure 6.3: Probability distribution of arrival delay at B
103
6.1.1.2 Departure Delay at B
We can distinguish between 2 cases:
+S =2.5: in this case, there will be no departure delay.
.
Sa,+Sg <2.5: in this case, there may be a departure delay.
Since the maximum actual transit time on AB is 2 hours, and the turn time is required to
*
be at least 0.5 hours, the plane is guaranteed to depart on time at B if
Sa,
+
S9 =2.530.
The probability distribution of the departure delay at B is shown below.
P(delay=O)= Sab+Sg-1.5
1
0
2.5 Sa
5g
departure delay at B (min)
Figure 6.4: Probability distribution of departure delay at B
6.1.1.3 Elapsed time between scheduled departure at B (thb)
and arrival at A
The distribution of the elapsed time between the scheduled departure time at B and the
actual arrival time at A is illustrated in Figure 6.5. The distribution is obtained by using a
convolution of the probability density functions of departure delay at B and actual transit
time from B to A.
30
Note that it would never make sense to have
Sa +S >2.5.
104
0.5
.......... 4 ....................
0.5(Sab+Sg-1.5)
..........
0.5(2.5-Sab-Sg)
..........
...........................
..........
1
3.5-Sab-Sg
5.5-Sab-Sg
3
Figure 6.5: Probability distribution of elapsed time between scheduled departure at B
) and arrival at A (Cases 1 &2)
ttdd
6.1.1.4 Arrival Delay at A
In order to compute the probability distribution of arrival delay at A, we distinguish
between 3 cases:
.
Case 0: Sab +Sg=2.5
In this case, the airplane always departs on time from B. Therefore, the probability of an
arrival delay at A only depends on the scheduled time from B to A,
P(delay-0)=:
0.5
S,..
(Sba-1)
0.5
arrivadelay at A (min)
3-Sba
Figure 6.6: Probability distribution of arrival delay at A (Case 0)
.
Case 1:
S
+ S,
0.5
0.5(Sab+Sg+Sba-2 .5
<2.5 and 1
Sba
..........
3 .5
- S
- S
P(delay=0)- (Sba-1)(2Sab+2Sg+Sba-4)/4
I
0.5(2.5-Sab-Sg)
3.5-Sab-Sg-Sba
3-Sba
5.5-Sab-Sg-Sba
arrivql delay at A (min)
Figure 6.7: Probability distribution of arrival delay at A (Case 1)
105
.
Case 2: S,+ S <2.5 and
3 .5
- Sa-
_Sg
Sa
3
P(delay=O)= (2.5-Sab-Sg)(Sab+Sg-0.5)/4+(Sba-3.5+Sab+Sg)/2
0.52
0.5(2.5-Sab-Sg)
3-Sba
5.5-Sab-Sg-Sba
arrival delay at A (min)
Figure 6.8: Probability distribution of arrival delay at A (Case 2)
6.2 Objective functions
This section discusses important types of objective functions that can be used to
minimize delays relative to schedule on the A to B to A route. Four objective functions
are examined in detail.
We will define the parameters used in the objective functions as follows:
*
K: the penalty cost in $ incurred if the total scheduled time from A to B to A exceeds
a maximum duration, D. This penalty cost would typically exist in order to ensure
adequate aircraft utilization, or that a crew will not be over-scheduled. In our particular
example, D will be set equal to 4 hours.
. L: the penalty in $/flight associated with being "late" at A or at B, for some specified
amount of "lateness" (0 minutes, 15 minutes, etc.).
. F: the cost in $/hour of delay at A or at B.
*
Ca: the cost in $/scheduled block hour.
Ca: the cost in $/hour of scheduled turn around time.
We shall also introduce a new binary decision variable, 6 , which will be used to indicate
whether
a maximum
Sab +Sg +S,
31
duration
4+ M.9 ",
constraint
is
satisfied
or
not.
The
constraint,
is useful for enforcing a penalty cost, if the optimal
M here is an infinitely large number.
106
scheduled times exceed the maximum duration D (4 hours in this example). When the
total scheduled time is under 4 hours, 6 =0. When the total scheduled time exceeds 4
hours, 6 =1 and a penalty cost of $K is incurred, as mentioned above.
In this particular example, we chose to use D = E[Sb]
E[Sab]=l.5 hours, SgMIN=0.5 hours, and
E[S,]
+ Sg,MN+
E[Sba],
with
=2 hours. A maximum duration of 4
hours assumes a relatively efficient utilization of the aircraft. In retrospect, it is
conceivable that the maximum duration value chosen (D=4 hours) was not the best
choice. Future work could consist of examining how solutions would change with a
different cutoff limit (such as 4.5 hours or 5 hours).
6.2.1
Obiective Function 1
Objective Function 1 (OF 1) assumes that a late flight at B or at A is penalized by the
same amount L, regardless of the amount of delay. In this case, the plane is considered
late if its actual arrival time exceeds its scheduled arrival time. This implies the following
objective function:
Min K. 5 + L. P(late at B)+ L. P(late at A) ....................................
(OF 1)
where 3=1 if Sab + Sg + Sba > 4 and J=0 otherwise.
The above objective function assumes that delays are undesirable at both locations A and
B. Such an objective function encourages robustness and leads to slack building in the
schedule on the first leg of the trip or in the ground time, to ensure minimal propagation
of delays from B to A.
Table 6.1 shows the case-specific details of the expressions P(late at B) and P(late at A).
107
Sab + S
Case
Sab +Sg 2.5
2 .5
Sab + Sg + Sba
Sa + S
Case2
3
.5
at B)
2.5
Case 0
2.5
Sab +Sg
P(late at A)
P(late
Case Conditions
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
2
2 Sab
-
( 3 -Sba)/
2 -Sab
I -(Sa -1).(
2 -S
(2.5-Sa -S,)
2 Sal
+ 2 Sg + Sa -4)/4
3.5
2
/4+(3- Sba)/2
+ Sba
Table 6.1: Objective Function Terms for Objective Function 1
6.2.2
Objective Function 2
Objective Function 2 (OF 2) again assumes that a late flight, regardless of the amount of
delay incurred, is penalized by the same amount L. In objective function 2, however, a
plane is considered delayed if its actual arrival time exceeds its scheduled arrival time by
more than 15 minutes (0.25 hours). This rule is similar to that used by the US DOT. This
is captured by the following objective function:
Min K. 6 +L. P(latei5 at B)+ L. P(late 5 at A).........................................(OF
2)
with 6 defined in the same way as in (OF 1).
Table 6.2 shows the case-specific details of the expressions P(latei5 at B) and P(latel5 at
A).
108
Case
la
Case
lb
Sab+Sg= 2 .5
5
ab
+Sg
2.5
Sab + S, + Sba
2.5
seSab +S,
Case 3.5 - Sa +S
g
2aab
3
3.5
3
1-(Sba-).(2 Sab+ 2 Sg
Sba
- (Sab +
MAX(0,.75 - Sab)
S9 +
+Sba -4)/4
Sba-2.375)/8
I -( 2 .5 - Sab - S,).(Sab
+ Sg -0.5) / 4
-(Sab + S, + Sba - 3.25) / 2
3.5
MAX(0,1.75 - Sab)
( 2 .5 - Sab - Sg) 2 /4 +(2.75
MAX(0,1.75 - Sab )
(5.25 - Sab - S9 - Sba)' /
MAX(0,.75 - Sah )
0
Sb) /2
5.25
a
2.5
-Sba < 0.25
2.5
sab + S, + S
<
3
MAX(0,1.75 -Sab )
-Sb,)/2)
Sab + S, + Sba < 5.25
Sab +S
Case
2c
MAX(0,(2.75
0.25
-Sba
sab +Sg
Case
MAX(0,1.75 - S,)
3.25
2.5
Sab+ Sg
3.25 < Sab + S + Sba
P(lateis at A)
P(late 5 at B)
Case Conditions
Case
0
> 5.25
a
-Sa<0.25
Table 6.2: Objective Function Terms for Objective Function 2
6.2.3
Objective Function 3
In Objective Function 3 (OF 3), the cost of delay increases linearly with delay time. F
represents a penalty cost in dollars per hour of expected delay. Note that a plane is
considered late if its actual arrival time exceeds its scheduled arrival time. This implies:
Min K. 3 + F. E[minutes of delay at BJ+F. E[minutes of delay at A].............(OF 3)
with 6 defined in the same way as in (OF 1).
Table 6.3 shows the case-specific details of the expressions E[min delay at B] and E[min
delay at A].
109
Case Conditions
Case
Sab+Sg= 2 . 5
Eldelay at A]
E[delay at
BI
(2 - Sb) 2 /2
(3- Sb,)2
(2-Sab ) 2 /2
( 3 .5-
/
0
Sab + Sg
Case
1
Sab +
Sg + Sba
+(
3.5
6
2
Sb - S9 - Sa ) .(Sb + S9 + Sba
.5-Sab -S9 -
(11.5-
Sab +Sg
2
2.5
Sab
2.5
2
(2-Sab ) /2
+Sg + Sba > 3.5
3
Sba
-
2
Sab-
Sba).(Sab + S
-0.5)/4+
Sg ).(2.5 - Sab - Sg)
(3-Sba )2 / 4 +(11.5 - 3Sba
( 2 .5-Sab -S
-0.5)/12
2
/12
Sab -Sg)*
)2 /12
Table 6.3: Obiective Function Terms for Obiective Function 3
6.2.4
Objective Function 4
includes
In addition to incurring a penalty per delayed flight, Objective Function 4 (OF 4)
that a
a cost per hour for scheduled time in the air (Ca) and on the ground (Cg). Note
plane is considered late if its actual arrival time exceeds its scheduled arrival time. This
translates into the following objective function:
Min K. J+ L. P(late at B)+ L. P(late at A)+ C.
(Sb +
Sb,)+ Cg. Sg.........(OF 4)
with 6 defined in the same way as in (OF 1).
See table 6.1 for case-specific details of the expressions P(late at B) and P(late at A).
at both A
All four objective functions described in this section imply that if a flight is late
gives
and B, it will get penalized twice for the delay. This type of objective function
be
incentives to avoid delays on the first leg of the trip (A to B). Note that it would
for
possible to use different penalty costs for being late at different locations to account
for being
the fact that some locations are more important than others, for example $La
equal
late at A and $Lb for being late at B. However, in our example, we will assume
costs ($L) for both locations A and B for simplicity.
110
6.3 Results:
In order to come up with the optimal results corresponding to each objective function, we
looked analytically at the different cases and further subdivided them into cases where
J =0 and cases where S 1. Each sub-case's optimal solution was then derived using a
combination of Excel Solver and trial and error.
Objective Function 1
6.3.1
The mathematical programming problem corresponding to objective function 1 is as
follows:
Min K. 8 + L. P(late at B)+ L. P(late at A)
s.t
I
S ab
2 ................................................................................
(i)
1 Sba < 3 ................................................................................
(ii)
S,
0 .5 ...................................................................................
(iii)
Sab +
S + S , 4 + M .5 ...............................................................
(iv)
S e {0,1}...............................................................................
. .. (v)
In addition to constraints (i)-(v), case-specific constraints (in the "conditions" column of
Table 6.1) are also added, depending on the case considered.
Solutions on a case-by-case basis are shown in Table 6.4.
111
Optimal Solutions (OF 1)
Case 0
2, S
S
Obj =0.75L
6=0
= 1.5 S = 0.5
Case 1
2 Sa = 1, S = 0.5
I
Obj = L
Case2
Sa
,Sba =1.5, S =
6=1
3 , Sg = 0.5
Obj = K
ab =
2
Sa
= 2 ,a=
0.5
32
Impossible
S
=
2
=
,Sba,
3S9 = 0.5
Obj = K
Obj =0.75L
Table 6.4: Solutions for Objective Function 1
As expected, for large values of L relative to K (i.e., when the airline strongly favors ontime performance achievement over high aircraft utilization rates), the airline will ensure
that schedules are such that delays are minimized. Because the penalty cost for exceeding
the maximum duration, D, is a lump sum and does not depend on the magnitude of the
duration by which the maximum is exceeded, scheduled times are set to the maximum
possible duration of actual transit times, to ensure a null probability of delay. Note that
this would not necessarily be the case if the penalty depended on the magnitude of the
time by which maximum scheduled duration was exceeded.
As can be seen in Table 6.4, the relative values of K and L will determine which
scheduling strategy the airline should choose.
If K / L 0.75, then the optimal solution is Sh 2, Sb, =1.5, S9 0.5. The objective
function has the optimal value of 0.75L.
0.75, then the optimal solution is Sb =2, S,= 3, S9=0.5. The objective
. If K /L
.
function has the optimal value of K.
As expected, both optimal strategies consist of scheduling the first leg of the trip (A,B)
for the largest possible observed duration. This makes sense, as arriving late at B results
in a double-penalty in some cases. When there is not enough slack, arriving late at B
implies departing late at B, which results in a higher probability of being delayed arriving
at A.
32
1 by definition would never have delta=1, because case I is such that
+ Sg + Sba 3.5
Note that case
2.5
Sah
112
Objective Function 2
6.3.2
Min K. 6 + L. P(latel5 at B)+ L. P(lates at A)
s.t
I Sab
2 ......................
1 Sba
3 ...............................................................................
. . . . . . . . . . . . .. . . .. .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .. . .. .
( i)
0 .5 ...................................................................................
S9
Sab + S, + Sba
()
(iii)
< 4 + M .J ...............................................................
(iv)
. . (v)
J c {0,1}..............................................................................
In addition to constraints (i)-(v), case-specific constraints (in the "conditions" column of
Table 6.2) are also added, depending on the case considered.
Solutions are shown in Table 6.5 below.
Optimal Solutions (OF 2)
8=1
8=0
C ase
0
5
1.7 5, Sb, =1.5, S9 = 2 . - Sab **
Obj = 0.625L
Sab 1.75, S la 2.75,S9 = 2.5 - Sab
Obj = K
1. 7 5 , Sba = L,S = 0.5
Obj=0.8906L
Impossible
=1. 7 5, b, = 1.25, Sg = 0.5
Obj=0.7656L
Impossible
Sab
Case
la
Sa
Case
Sab
Case
2a
Sab =1.75,Sb,
lb
Case
2b
Case
2c
**
=1.75, S, = 0.5
Sab
1.75,SU =2.75,S
Obj= 0.5156L
Obj= K
Impossible
Sab
= 2.5 - Sab
1 .7 5 , Sba 2.75, S9 = 5 .2 5 -
Sab
Sba
Obj= K
Impossible
1. 7 5 , Sa
Obj= K
Sab
2.75, S9 = 2.5 - Sab
multiple solutions
Table 6.5: Solutions for Objective Function 2
113
The optimal schedule will depend on the relative values of K and L.
.
If K / L > 0.5156, the optimal solution is Sah=1.75, Sba=1.75, S9=0.5. The objective
function's optimal value is then 0.5156L.
.
If K / L
SabI
0.5 156, there are multiple optimal solutions. Solutions such that
1.75, S9 =2.5-Sab, and SbU 2.75 will all yield an objective function equal to K.
As expected in this case, the optimal solution is such that S.b is always greater or equal
to 1.75, ensuring no delay at B. However, it is interesting to note that the optimal solution
when K / L
0.5156 is such that some departure delay at B may be incurred, potentially
causing a propagation of delays.
6.3.3
Objective Function 3
Min K. S + F. E[minutes of delay at B]+F. E[minutes of delay at A]
s.t
1 S ah < 2 ................................................................................
1 S
S,
S.a
< 3 ................................................................................
<a
0 .5 ...................................................................................
+
S
+ Sa
! 4 + M .S ...............................................................
3 ( {0,1} .....................................................................................
(i)
( 1)
(iii)
(iv)
(v )
In addition to constraints (i)-(v), case-specific constraints (in the "conditions" column of
Table 6.3) are also added, depending on the case considered.
In summary, we have:
114
Optimal Solutions (OF 3)
=0
Case
= 2Sa =1.5S9 =g0.5
S
Obj =0.5625F
Case 1
Case22b
____Obj
=1.562,Sba=1.438, S9 = 0.5
Obj= 0.7878F
Sab
Sab -1.6375,Sa = 1.8625, S =0.5
ab
'
=0.4305F
S=1
Sab =
2
,S
= 3,S9
=0.5
Obj = K
Impossible
Sab = 2,Sba =3,S9 =0.5
= K
Obj =K
Table 6.6: Solutions for Objective Function 3
Once again, the optimal schedule will depend on the relative values of K and L.
.
If K/F>!0.43, the optimal solution is
S,=1
.64,
Sha=.86,
S9=0.5.
The
corresponding objective function value is 0.43F.
*
If K /F < 0.43, the optimal solution is Sab=2, SbU=3, S9=0.5. The corresponding
objective function value is K.
Note that in the optimal solution for K /F
0.43,
Sab
is no longer scheduled to its
maximum 2 hours duration.
Objective Function 4
6.3.4
Min K. 6 + L. P(late at B)+ L. P(late at A)+ Ca.(
b + Sba
)+ Cg. Sg
s.t
I
Sab
2 .................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... (i)
1 Sba 3 ................................................................................
(ii)
S,
0 .5 ...................................................................................
(iii)
Sab +
S
(iv)
+ Sba < 4+ M.8 ...............................................................
s1 {,1 } .....................................................................................
(v )
115
In addition to constraints (i)-(v), case-specific constraints (in the "conditions" column of
Table 6.1) are also added, depending on the case considered.
In this case, optimal solutions will depend on the relative values of L, K, Ca, and Cg.
6.3.4.1 Case 0
Figures 6.9 and 6.10 illustrate the optimal solutions obtained for Case 0. The lines define
the boundaries between families of optimal solutions. The lines represent combinations of
factors L, Ca and C9 for which there exist multiple optimal solutions.
CaseO, delta=O
----
10
9
8
--
-
-
-
-
-
-
-
-
-
--
-
~----
7
5
30
2
1
0
0
1
2
3
Sab=2, Sba=1, Sg=0.5
Sab=2, Sba=1.5, Sg=0.5
- -Linear (Sba=1, Sab+Sg=2.5)
4
6
5
*
+
-
-
7
8
9
10
L/Cg
Sab=1, Sba=1, Sg=1.5
Linear (Sab=2, Sg=0.5, 1<=Sba<=3)
Figure 6.9: Optimal solutions for Case 0, =0
116
CaseO, delta=1
4'
10
9
. ~.
Rgo
8
7
,
p0
p
t
6
5
0)
U
(U 4
(3
3
2
1
0
0
-
+
*
1
2
3
4
Sab=2, Sba=1.5, Sg=0.5
Sab=1, Sba=1.5, Sg=1.5
Linear (Sab=2, Sg=0.5, 1<=Sba<=3)
5
6
-
-
7
8
9
1 L g
Sab=2, Sba=3, Sg=0.5
-Linear (Sba=1, Sab+Sg=2.5)
Figure 6.10: Optimal solutions for Case 0, 6=i
Figures 6.9 and 6.10 show that the optimal solutions will depend on the relative values of
L, Ca, Cg, and K.
6.3.4.2 Case 1
Given the definition of Case I (Sab + Sg
2.5 and 2.5
Sab
+ Sg + Sba
3.5) 6 is always
equal to zero. Figure 6.11 shows there are 2 families of optimal solutions, depending on
the relative values of Ca/Cg and UJCg.
117
Casel, delta=O
,,,
- _jGc3
9
81
C 4
--
-
32
31
+
A-+
-
- --
0
A
-
-
Sab=2, Sba=1, Sg=0.5
m
-Linear (1<=Sab<=2, Sba=1, Sg=0.5)
9
8
7
6
5
4
3
2
1
0
10
LCg
Sab=1, Sba=1, Sg=0.5
Figure 6.11: Optimal solutions for Case 1, 5 =0
6.3.4.3 Case 2
Case2 delta=O
Ir.0
10
--
9
7
-
--
-6-
8
+
4
4
------
-+-
u-+-5-
,i
++
-
-
6
5
0
jC9
A
3
2
0
0
*
1
2
3
4
5
6
7
8
9
10
Sab=1, Sba=1, Sg=1.5
*
Sab=2, Sba=1.5, Sg=0.5
- - *Linear (Sba=1, Sab+Sg=2.5)
Sab=2, Sba=1, Sg=0.5
Linear (Sab=2, Sg=0.5, 1<=Sba<=3)
Figure 6.12: Optimal solutions for Case 2, 6 =0
118
=2W
delta=1
CEse2
10
9
8
7
4
p
-
-
-
----
Ar-e
*o
6
05
04
3
2
p
1
0
p
1I
3
2
U
Sab=2, Sba=3, Sg=0.5
M M Sab=2, Sba=1.5,Sg=0.5
0
4
6
5
+
7
8
LAg
9
10
Sab=1, Sba=1.5, Sg=1.5
Linear (Sab=2, Sg=0.5, 1<=Sba<=3)
-Linear (Sba=1, Sab+Sg=2.5)
Figure 6.13: Optimal solutions for Case 2, 6 =1
6.3.4.4 Summary
Table 6.7 summarizes the case-specific optimal solutions and corresponding objective
function values.
119
Optimal Solutions (OF 4)
Additional
Conditions
Ca CC + L
Case
0
0.5L< C
Ca
Ca
Case
1
Cg + L
0.5L
6=0
Sab =1, Sba =1,S =1.5
Sab =1,Sba =1.5, S9 = 1.5
Obj
2L + 2C, +1 .5C
Obj = K +1.75L + 2.5Ca +1.5C9
Sab
2,SI
Sab = 2 ,,
=1.5,S9 = 0.5
Obj=L+3Ca+0.5C9
Obj=K+0.75L+3.5Ca+0.5C
Sab= 2Sba =1.5, S9 =0.5
Sab =2,S, = 3,S
Obj = 0.75L + 3.5C, + 0.5C9
Obj = K + 5C, + 0.5C9
Impossible
= 0.5
Obj =2L + 2C, + 0.5C9
Sab= 2 Sba = 1,Sg = 0.5
Ca L
Obj
Ca
Case
2
=1,S = 0.5
Sab =1,Sba =Sg =0.5
L
6=1
0.5L
CO
C
0.5L
=L + 3Ca +0.5C9
Sab =, S b
C +L
C, + L
Impossible
= 1,S9 = 1.5
Sab 1,Sa =1.5, S9 =1.5
Obj =2L + 2C, +1.5C9
Obj
Sab = 2 ,Sba =, S = 0.5
Sa= 2,a
Obj =L +3C +0.5C
Obj
K +0.75L + 3.5C +0.5C9
Sab= 2 S=
Sab
2
1.5, S9 = 0.5
K +1.75L + 2.5C +1.5C9
=
1.5, S9 = 0.5
,Sba = 3, S9 = 0.5
Obj= K + 5C, +0.5C9
Obj =0.75L + 3.5Ca +0.5C9
Table 6.7: Detailed case-by-case optimal solutions for Objective Function 4
Table 6.7 can be further reduced to Table 6.8, in which optimal solutions are not casespecific, and only depend on the relative values of K, L, Ca, and Cg (Table 6.8):
120
Optimal Solutions (OF 4)
Sob =,Sba = s = 0.5
Ca >!L
0.5L & Ca
Obj = 2L + 2C, +0.5C9
2
Sb = ,'Sa = 1, Sg = 0.5
L
Obj =L + 3C, +0.5C9
If K
0.75L -1.5C:
Sob= 2,Sb,
Ca
0.5L
1.5,S9 = 0.5
Obj =075L + 3.5Ca +0.5C9
If K 0.75L-1.5Ca :
Su= 2,Sba = 3, S9 = 0.5
Obj =K + 5C, + 0.5C9
Table 6.8: Optimal solutions for OF 4 as a function of K, L. Ca, and C.
The objective function was more complex in this case. This resulted in the optimal
schedule depending on the relative values of a larger number of parameters. In the
optimal solution,
Sab
is not always set equal to its maximum possible value. It is
beneficial to have it equal to this maximum to ensure on-time departure at B and reduce
delay propagation. However, when there is a cost associated with flying time, it is not
necessarily cost minimizing for the airlines to fix Sa, equal to its maximum.
6.4 Conclusions
This simple example illustrates the impact of the choice of an objective function on the
optimal schedule. There are many more potential objective functions that could be
considered, depending on the variables and parameters that the scheduler wishes to
capture. Objective functions reflect the priorities schedulers have. Depending on whether
they want to reduce expected minutes of delay, or the probability of delays, and
depending on how they value time spent in the air as opposed to time spent on the
ground, they will make different scheduling decisions.
121
In our example, scheduling solutions depend on the relative perceived costs of aircraft
utilization and cost of delays. As expected, if the perceived cost of delays is much greater
than the cost of foregoing efficient aircraft utilization, then optimal scheduled transit
times on each leg are set to the corresponding maximum actual times observed on this
leg. This observation is only valid for objective functions 1-3, and only valid because the
penalty cost incurred for exceeding the maximum scheduled duration does not depend on
the amount by which it is surpassed (as noted earlier). Results obtained show the
importance of ensuring that the schedule minimizes the delay on the first leg of the trip,
in order not to propagate delays on the remaining legs.
Future directions of research could consist of examining the effect of:
o
varying the value of the maximum scheduled duration parameter.
o
introducing a penalty cost that would increase with the amount by which
the maximum scheduled duration is exceeded.
o
introducing different delay costs on the different legs of the trip to
emphasize the relative importance of being on time at different locations.
In this chapter, we demonstrated the complexity of scheduling an airline route so as to
minimize delays relative to schedule. This was done through a very simple example (one
airplane making a round trip, and uniform trip time distributions). In reality, airlines deal
with extensive networks of routes. Moreover, in most cases, reducing costs is not the
airline's only consideration. Schedules are also driven by efforts to coordinate the
number of flights in each connecting bank at hub airports, and are also designed with the
competitors' schedules in mind. It is also important to point out that the probability
distributions of transit times on given O-D pairs are complex and evolve over time (as
shown in Chapter 3), making it even more difficult for airlines to determine an optimal
schedule.
122
CHAPTER 7: CONCLUSION
7.1 Summary
In Chapter 1, we argued that schedule adjustments prevent the commonly reported
statistics on flight delays relative to schedule (such as the US DOT measure) from being
used in a number of contexts. They cannot be used to estimate the true extent of air traffic
delays or to gauge the state of the airspace and air traffic control systems, since they do
not account for congestion-related delays. This motivated us to develop an alternative
delay metric. We determined that the new measure should consist of taking the difference
between the actual gate-to-gate time and a consistent benchmark that would approximate
the congestion-free time.
In Chapter 2, we discussed appropriate estimates for the benchmark, after considering the
factors affecting the variability of gate-to-gate travel times.
Given that our primary
interest lies in identifying long-term trends and changes in "true" delay, we decided not
123
to concern ourselves with day-to-day fluctuations due to periodic factors (seasonality,
day-of-the-week, and time-of-day) or to stochastic factors (weather/winds, runway and
gate assignments, and flight path). We also decided not to concern ourselves with the
impact of aircraft type on gate-to-gate variability, since all data used referred to jet flights
and the substitution of one jet type for another seems to have only a small impact on
travel times. We then suggested and discussed alternative measures that could be used to
estimate the congestion-free baseline times. After examining several possibilities, it was
decided that for our purposes it would be most appropriate to use a percentile of gate-togate time in the 5-20% range.
In Chapter 3, we outlined the procedure used to define consistent O-D-specific baseline
times. We computed the baseline times for each of the 618 O-D pairs under consideration
using the fifteenth percentile of gate-to-gate time, averaged over a four-month period. We
then computed "true" O-D delays by taking the difference between actual gate-to-gate
time and the baseline, and analyzed their evolution from 1995 to 2000. We found that the
average "true" delay on the 618 O-D pairs increased from 11.1 minutes per flight in 1995
to 16.9 minutes in 2000 (52% increase). On 75 of the 618 O-D pairs considered, true
delays more than doubled over the 1995-2000 period. When "true" delays were compared
to delays relative to schedule, we found that "true" delays were about 40% to 60%
greater than delays relative to schedule. Analysis of "delays relative to scheduled transit
time" and "delays relative to schedule" suggested that although airlines seem to be able to
accurately predict gate-to-gate times, they are not good at predicting departure times,
which may be the reason why delays relative to schedule are incurred.
In Chapter 4, we described two different methodologies to attribute O-D delays to the
airports of origin and destination. The first method is an iterative method based on the
attribution of a variable portion of the overall O-D delay to the airports of origin and
destination, depending on the relative congestion at those airports. The second method is
based on the decomposition of gate-to-gate time into its three components (taxi out time,
124
airborne time, taxi in time), the calculation of individual component delays, and the
attribution of component delays to the relevant airport. Results obtained using both
methods showed that airport delays increased over the 1995-2000 period: the average
increase in delays at the 27 airports considered was of the order of 2 to 3 minutes per
operation, which represents an increase of 40% to 53% depending on the method used.
Further analysis on individual component delays suggested that there was a strong
correlation between taxi out delay and airport of origin, as well as between taxi in delay
and destination airport, confirming our decision to attribute taxi out (taxi in) delay to the
origin (destination) airport. The second methodology also suggested that about 60% of
the airborne delay on any given O-D route is attributable to airspace congestion whereas
the remaining 40% is attributable to the destination airport.
In Chapter 5, we showed two applications of the methodologies outlined in Chapters 3
and 4. In the first application, we estimated total annual delays at Logan airport (BOS)
using average delay figures obtained from Chapter 4. Our best estimates showed that
annual "true" delays at Logan doubled from 1995 to 2000: "true" delays were on the
order of 80,000 to 105,000 hours for the year 2000, up from 40,000-45,000 hours for
1995. This application can be extended to all 27 airports covered in this study. In the
second application, we derived delay-rankings of airports based on the individual airport
delays obtained in Chapter 4. We then compared our rankings with the FAA's and DOT's
airport rankings (such as OPSNET delays, ASPM delays, etc) using the Spearman
correlation test. Results suggested that ASQP on-time statistics and average delay relative
to schedule are poor indicators of the true extent of air traffic delays. We were surprised
to observe that, although OPSNET statistics severely underestimate delays, they yield
very similar rankings to those obtained using the methods we derived in Chapter 4. This
suggests that OPSNET statistics can be useful in determining the relative extent of
congestion at different airports.
In Chapter 6, we focused on delays relative to schedule and showed why it may be very
difficult for airlines to optimize their schedules so as to achieve high schedule
125
compliance records. We used a simple case (an aircraft scheduled for a round trip,
uniform probability density functions for actual transit times) to point out some of the
complexities and interdependences in the schedule that make airline scheduling so
complex. We also showed how the choice of the objective function impacted the optimal
scheduling solution obtained. In our example, scheduling strategies depended on the
relative perceived costs of reduced aircraft utilization, on the one hand, and of delays, on
the other. Results obtained in our example showed the importance of ensuring that the
schedule minimizes the delay on the first leg of the trip, so as to avoid the propagation of
delays on the remaining legs of an aircraft's itinerary.
7.2 Future Research Directions
The work described in this thesis can be refined and extended in many different ways.
Further research directions are discussed below.
7.2.1 Derivation of the baseline
In this thesis, we chose to use the fifteenth percentile of gate-to-gate time in order to
compute the baseline. However, as indicated in Chapters 2 and 3, any percentile in the 520 range might be equally appropriate. Although it was argued that the exact value of the
baseline is not especially critical to our measure of the evolution of true delays, it would
be interesting in the future to refine our choice of percentile and examine the sensitivity
of the delay results computed to the percentile chosen.
The choice of the sample over which the baseline time is estimated could also be refined.
In this thesis, we chose to use a sample of flights that covered the whole day (24 hours) to
derive the baseline. Another approach could have been to take a sample of flights
operating at times that are believed to be congestion-free, since our goal is precisely to
estimate congestion-free times. One could explore the use of a "restricted" sample of
126
flights operating on days that are least traveled (Saturdays) or during off-peak (after 9
PM), to ensure that the baseline derived does not encompass any congestion delay.
More detailed analysis on the impacts of the various factors affecting gate-to-gate
variability (as identified in Chapter 2) could be performed. Derivation of seasonal
baselines to account for the variability in gate-to-gate time due to seasonality could be
explored. The effect of aircraft type substitution could also be investigated more closely,
since the impacts of the introduction of large numbers of regional jets may, in the future,
prove to be significant, on routes where these jets replace non-jets.
7.2.2 Extension of the analysis
In this thesis, all analysis and computations have been performed for flights operating on
a sub-network of 618 O-D pairs between 27 major airports. Analysis could be refined and
extended by including more airports, for example, the 50 busiest airports in the US, or
even every airport on which airlines regularly report data. Extending the analysis could
allow one to monitor the approximate size of delays nationally or at additional individual
airports. This would be useful in assessing whether the airport system and the air traffic
management system (ATM) are keeping up with traffic growth on aggregate.
Currently the bulk of the analysis was performed for years 1995, 1997, and 2000. It
would be very interesting to extend the time horizon and estimate delays after September
11, 2001 to test the validity of the methodologies. One would expect to see a decrease in
"true" delays, as traffic levels and congestion decreased nationally after this date.
Finally, the application described in Chapter 5, which consists of calculating total annual
delays at Logan airport, should be extended to all airports. Note that total annual delay
estimates are based on the untested assumption that all flights, whether general aviation
or commercial, experience delays similar to those of jets flown by major carriers. This
127
assumption needs to be validated and a future direction of research could consist of
computing separately delays for regional carriers and general aviation operations.
7.2.3 Scheduling to minimize delays relative to schedule
As discussed in Chapter 6, the probabilistic model derived could become more insightful
if the following directions of research were explored:
.
using probability density functions based on historical data for actual trip time
instead of using uniformly distributed trip times;
.
varying the value of the maximum scheduled duration parameter (which is
currently set to 4 hours) to values of 4.5 hours or 5 hours and examine the impact
on the solutions obtained;
.
introducing a penalty cost that would increase with the amount by which the
maximum scheduled duration is exceeded;
.
introducing different delay costs on the different legs of the trip to emphasize
the relative importance of being on time at different locations.
128
REFERENCES
Booz-Allen & Hamilton (2001)- "Punctuality: how airlines can improve on-time
performance."
Mayer and Sinai (2001)- "Hubbing versus the 'Tragedy of the commons': why does
every flight by US Airways from Philadelphia seem to be late?"
Shumky (993)- "The response of US carriers to the DOT on-time disclosure rule"
Willemain, Thomas (2001)- "Estimating the Components of Variation in Flight Times"
http://www.bts.gov/
http://www.faa.gov/apa/janOldel.htm
http://www1.faa.g-ov/events/benchmarks/
httr://www.massport.com/
129
130
APPENDIX A: NOTATION
Notation used: i: origin airport; j: destination airport.
PERCENTILES
Px
tm,y)
A Pi,' (y)
_xt percentile of gate-to-gate
time on (ij) in a given month
m for year y
Average xth percentile of
AFj7 (95)=
( Po (1,95)+ Pj (4,95)+ Po' (7,95)+ PIj (10,95))/4
gate-to-gate time on O-D pair
(ij) in year y
4Px(97)='(1,97)+
(4,97)+
APx (oo)= ( Px (1,00)+ P
(4,00)+ Pi7(7,00))/3
(7,97)+
Bx:
BASELINE
Ax (97), A(oo))
AP(95),
BX =MIN
O-D pair
forpercentile
Baseline
A
i'
B
the xh
(ij) usingtime
WB :
Weighted baseline per airport
WBx =
WB
Overall weighted baseline
using the xth percentile for
WB x = (
L
of origin using the x
percentile for all O-D pairs
originating at I
P(10,97))/4
BB( * TF.(00))/(Y TF (00))
B * TF (00)) /(Z E TF, (00))
,
i
ALL 618 O-D pairs
FLOWN FLIGHTS
F, (m,y)
number of flown flights in
month m of year y
TF, (y)
number of flown flights in
year y for the months
considered
TF,
(95)=
F
(1,95)+
F
(4,95)+ FU (7,95)+
F
(10,95)
TF (97)= F 1,97)+F 1 (4,97)+F (7,97)+ F (10,97)
TF1 (oo)= Fj (1,oo)+F (4,00)+ F (7,00)
GATE-TO-GATE TIMES
Gi1 (m,y)
average of actual ASQP gateto-gate time from origin i to
destinationj during month m
ofyeary.
A Gj (y)
weighted average of actual
AG
(oo) =(Gi
(1,00)* Fj (1,00)
ASQP gate-to-gate time
during year y
D' (y)
+G, (4,00)*F (4,00)+G (7,00)*
F
(7,00))!
O-D DELAYS
Dx (y)= A Gj (y)-B
Average O-D delay on O-D
pair (ij) in year y.
131
--awp-
WD'(y)
Weighted average per airport
WD' (y) =
WDLL (Y)
Overall weighted average of
delay using the xth percentile
WD
TF (y) * D' (y) /(Z TF1 (y))
of origin using the x
percentile for all O-D pairs
originating at I
for ALL 618 O-D pairs
LL (Y)
*
(YT
D
(y)
i j#i
/(Z TF(
(y))
i j#i
ATTRIBUTION TO AIRPORTS
OrgADJ (y)
DestAD (y)
Ax(y)
Average origin delay per
aircraft at airport a computed
using the xth percentile of
gate-to-gate time
OrgADJ(y) =(Y
Average destination delay per
aircraft at airport a computed
using the xth percentile of
gate-to-gate time
DestADx(y) =(
Average delay (whether
origin or destination) per
aircraft at airport a computed
Ax (y) =(
using the xth percentile of
gate-to-gate time
Z TF
i
D * TFaj (00))
(00)
Dx* TFI (oo))
Z TF, (oo))
DX * TF1 (oo)+
Z
D
* TF (oo)
i=aja,i
TF (00)
Z
TdZod
132
- - ivq
APPENDIX B: DETAILED RESULTS
B.1. SENSITIVITY OF THE BASELINE TO THE PERCENTILE CHOSEN
133
B.2. EVOLUTION OF "TRUE" DELAYS PER AIRPORT OF ORIGIN
134
B.3. COMPARISON "TRUE" DELAYS VERSUS DELAYS RELATIVE TO
SCHEDULE FROM 1995 TO 2000
135
B.4. SENSITIVITY OF ON-TIME PERFORMANCE STATISTICS TO DELAY
DEFINITION USED
136
APPENDIX C: AIRPORT DELAY ATTRIBUTION
Notation used: i: origin airport;
j: destination airport.
ATTRIBUTION TO AIRPORTS- METHODOLOGY A (Step Al)
OrgADla(y)
Average origin delay per
OrgADla(y)= 0.5*(
D (y)* TF,
aircraft at airport a, calculated
using Step Al
DestADla(y)
Average destination delay per
aircraft at airport a, calculated
TF (y))
DestAD5a(y)=0.5*
using Step A I
Average delay (origin and
destination) per aircraft at
airport a, calculated using
Step Al
Al (y)
(y>(
D
(y)*
TFa (y)
TF (y))
A1(y)= [ OrgADla(y) * (ZTF,, (y)) +
DestADla(y)* (
Z..,
TF (y)
ja (y))
1/
[TFia(y)+jTFia yW) ]
ATTRIBUTION TO AIRPORTS- METHODOLOGY A (Step A2)
CORG
(y Coefficient of origin
correction
CORGijter=0 (y) = OrgADl (y)/(
DestADl1 (y) + OrgAD1l (y))
CORGiter=k+ (y) = OrgAD2,= (y)1/
DestAD2,,erk (y) + OrgAD2jte,,,
CDES
(y Coefficient of destination
U~trk correction
CDESiie,=O (y) =
CEije=
y
(y))
DestAD 1 (y)/(
et
OrgADl, (y) + DestADl1 (y))
CDES i( er=k+l (y) = DestAD2, ,iter(y)
(
OrgAD2iiter.k ( y
DepDterk (y) Departure delay on O-D pair
DepD~jt..(y)
DestAD2 ,,erk (y))
CORGij,er= (y) * D,5
(i,j) using Step A2
ArrDijerk(y) Arrival delay on O-D pair (ij)
using Step A2
OrgAD2a(y)
Average origin delay per
aircraft at airport a, calculated
using Step A2
ArrD
(y)= CDESi ,terykY)* D
BY ITERATION:
k*
.
OrgAD2a,i=erk(y)= (I
TF
(y))(
DepD,,,,er(k (y)
TF, (y))
137
DestAD2a(V)
Average origin delay per
aircraft at airport a, calculated
using Step A2
BY IERATION:
iTER k:
DestAD2.,iter=k(y)=(j ArrDj
y)/
Average delay (origin and
destination) per aircraft at
airport a, calculated using
Aa2(y)
,
(y)*TF
YTF, (y))
Aa 2(y) = [OrgAD2. (y) * (yTFj (y)) +
DestAD2, (y) *
(
Step A2
[
TFj(Y)+
(y))
/
TF(y)) ]
Ii
ATTRIBUTION TO AIRPORTS- METHODOLOGY B (Step BI)
15"h percentile of taxi out time
PTO (m,y)
on (ij) in a given month m for
year y
5
PTI
5
PAIRyj
(m,y)
(m,y)
APTO 5 (y)
15 th percentile of taxi in time
on (ij) in a given month m for
year y
15th percentile of airborne
time on (ij) in a given month
m for year y
Average 15'h percentile of
taxi out time on O-D pair (ij)
in year y
APTOj5 (95)=( PTOQ (1,95)+
PT0 15 (4,95>+PTO 5 (7,95)+PTO (10,95)>/4
(,5+T,(09)/
PQ
(.9)PO
APTO, (97)=( PTO0,5 (1,97)+
PTO, (4,97)+PTOj5 (7,97)+PTOjt
(10,97))/4
APTO 5 (00)= (PTOt5 (1,00)+
5
PTOQ (4,00)+ PTO (7,00>>/3
APTIf 5 (y)
Average 15th percentile of
taxi in time on O-D pair (ij)
in year y
APTI 5 (95)=( PTI (1,95)+
FTP.1 (4,95)
APTIj (97)=(PTIV (1,97)+
PTI5 (4,97)+PTI5 (7,97)+PTI (10,97))/4
APTI5 (oo)= (PTIs (1,0)+
PTI.
APAIR 5 (y)
percentile of
airborne time on O-D pair
Average
15 'h
(ij) in year yj(49)
(4,00)+PT,5 (7,00))/3
APAIRIJ 5 (95)( PAI 5 (1,95)+
PAIRt 5 (4,95)+ PAIR; 5 (7,95)+PAIR
A jt(75)PI9 (10,95))/4
APAIR
(97)- ( PAIRi5 (1,97)+
PAIR;5 (4,97)+ PAIR 5 (7,97)+PAIR (10,97))/4
138
APAIR O (o0)=( PAIR5 (1,00)+
5 (4,00)+ PAIR
PAIRO
5
B TO15 :
Taxi out baseline time for OD
pair (ij) using the 15
percentile
BTO1 5 =MIN ( APTQ
BTI.5 :
Taxi in baseline time for OD
BTIj 5
pair (ij) using the
(7,00))/3
(95),
A PTO
(97),
APTO'. (00))
(95), APT
7)
(
1 5 th
percentile
BAIR 5MN ( APAIR 5 (95), APAIR 5 (97),
APAIR 5 (00))
BA IRy:
Airborne baseline time for
OD pair (ij) using the 15 th
percentile
TOy(m,y)
average of actual ASQP taxi
out time on O-D pair (ij)
during month m of year y.
TI (m,y)
average of actual ASQP taxi
in time on O-D pair (ij)
during month m of year y.
AIR1 (m,y)
average of actual ASQP
airborne time on O-D pair
(ij) during month m of year
y.
A TOy (y)
weighted average of actual
A TO (oo>=(
ASQP taxi out time during
year y
+T~i;(4,00)*
A TI (y)
AAIR
(y)
o y (1,00)* Fj (1,oo)
(4,oo)+ TOi;(7,00)* F, (7,oo))/
A T 1 (oo)= (TIi (1,00)* F, (1,oo)
weighted average of actual
ASQP taxi in time during
year y
+TI; (4,o)*F. (4,00)+TII
weighted average of actual
AAIRy (00) =(AIR y (1,00)* Fj (1,00)
ASQP airborne time during
year y
TF (oo)
+ AIRi (4,00)*
F
(4,oo)+
(7,00)*F
(7,oo)>/ TF, (oo)
A IR (7,oo)* F
(7,00))/
1
TF, (00)
D TO 5 A TOiy(y) - BTOOf
D TOI(y)
Average taxi out delay on 0D pair (ij) in year y.
D TI 5(y)
Average taxi in delay on O-D
D TI 5 A TI;(y) -BTIjj
DAIRY5(y)
Average airborne delay on 0D pair (ij) in year y.
DAIR,
OrgAD3,(y)
Average origin delay per
OrgAD3a(y)=
pair (ij) in year y.
aircraft at airport a, calculated
using Step B 1
Z
5
AAIRi
5
y) -BAIR1
TO (y) * Tlaj (y))
Y TFa, (y)
D(
I
i
139
DestAD3,(y)
Average destination delay per
aircraft at airport a, calculated
using Step Bi
DestAD3,(y)=
()
Average delay (origin and
destination) per aircraft at
airport a, calculated using
Step B 1
a
(y))*
T1 (y))/
TFi(Y))
(Z
Aa 3(y)
DAZR (y
(Z(DTk
Aa 3 (y)=[ OrgAD3, (y)*
DestAD3 (Y)* (I TF(y)
a Y
i
J
aTF
(y)) +
1/
[ZTF j(y)+ZTF (y))]
W)_________I
__________~~~i
ATTRIBUTION TO AIRPORTS- METHODOLOGY B (Step B2)
Correction coefficient that
CORRij(y)
CORR (y) = (BTO 5 + BTI1| + BAIR 1 )/ B15
takes into account the
correlation between taxi out,
taxi in, and airborne times.
OrgAD4a(y)
CORRaj (y) * D TO" (y)
Average origin delay per
OrgAD4a(y)=
using Step B2
* TFj
Average destination delay per
DestAD4, (Y)=(
CORR (y) (DTI ] (y) + DAIR
id (a
aircraft at airport a, calculated
DestAD4a(y)
aircraft at airport a, calculated
using Step B2
(y)))/
TFq (Y)
*TFia(y))/
Aa 4(y)
Average delay (origin and
destination) per aircraft at
airport a, calculated using
Step B2a
Aa 4(y)
5 (y))
TFia(y)
OrgAD4a(y) * (jTF
(y))+
DestAD4 (Y) * (E TF Wy)) ] /
Y
TFi,,(y))]
TFaj(Y)+
[
J
i
ATTRIBUTION TO AIRPORTS- METHODOLOGY B (Step B3)
DTO,15 (y)
Average taxi out delay on 0-
DTOQ1. 5 A TOy (y)-BTOQ 5
D pair (ij) in year y.
DTII.5(y)
Average taxi in delay on O-D
DTIg5 A5TI;(y-BTI; 5
pair (ij) in year y.
OrgAD5a (y)
Average origin delay per
aircraft at airport a, calculated
OrgAD5 (y)= OrgAD3, (y)
using Step B3
DestAD5a (y)
Average destination delay per
aircraft at airport a, calculated
using Step B3
DestAD5a (Y)=
(DTI (y)) *TF (Y))
(_ (DTI__(y))*_TF,_(y))/
TF (Y)
_TF __(y)
140
(Z(DTI " (y))* TFi,(y))/
A0 5(y)
TF,(Y)
Average delay (origin and
Aa 5(y)=[ OrgAD5a(y) * (Z TF (y)) +
airport a, calculated using
Step B3
DestAD5,(y) *
(
[ZTFj (y)+Z
TFia(y)) ]
destination) per aircraft at
TF,0 (y))] /
i
J
ATTRIBUTION TO AIRPORTS- METHODOLOGY B (Step B4)
DTO,(y)
Average taxi out delay on 0D pair (ij) in year y.
DTO,5 = A TOy;(y>- BT
D TIO5(y)
Average taxi in delay on O-D
D TI=5 A TIy (y) -BTIy
5
pair (ij) in year y.
DAIRy 5(y)
Average airborne delay on 0-
P
Fraction of airborne delay
attributed to the destination
airport
DAIR J5 AAIRJ
(y)-
BA1R 5
D pair (ij) in year y.
OrgAD6,(y, p) Average origin delay per
aircraft at airport a, calculated
OrgAD6,(y, p) =
1 () * TF
DTO(y
using Step B4
DestAD6, (y, p) Average destination delay per
A 0 6(y, p)
(Y)
T
aircraft at airport a, calculated
DestAD6, (y, p) =
1(Y) + p * DAIR1 (i))
using Step B4
(
(D Tid ()
(
TF,,(y))
(y))
Average delay (origin and
A0 6(y, p) = OrgAD6, (y, p) *
airport a, calculated using
DestAD6.(y, p)*
destination) per aircraft at
TF
*,
(
(
TF1 (y))+
TF, (y))] /
Step B4
[ZTF
0 j(y)+
_
_
_
_
_
YTF(y))]
_._
141
142
APPENDIX D: STANDARD DEVIATIONS
Notation used: i: origin airport;
j: destination
airport.
REMINDER
D TOj (y)
Average taxi out delay on O-D
pair (ij) in year y.
D TOJ 5 A TOi;(y)- BTO
DTIj;I(y)
Average taxi in delay on O-D
D TI= A TIiTjy) - BTIbj,
5
pair (ij) in year y.
5(y)
DAR 1 y~
Average airborne delay on O-D
SD2RG(TOy)
STANDARD DEVIATIONS
SD,0RG(TO,y)= -(DTO5
Standard deviation of taxi out
SDEST(TOy)
Standard deviation of taxi out
SDA)EST(TO,y)
=
SD9RG(TIy)
Standard deviation of taxi in
SDRG(TI,y)
a (D TI1 (y))
SDPEST(TIy)
Standard deviation of taxi in
SDEST(TIy)=o (DTIK
DAIR
AAIRi (y)- BAIR
pair (ij) in year y.
(y))
delays occurring on O-D pairs
departing at airport a
delays occurring on O-D pairs
arriving at airport a
delays occurring on O-D pairs
departing at airport a
(D TO5 (y))
(y)
delays occurring on O-D pairs
arriving at airport a
SDRG(AIR,y)
Standard deviation of airborne
SDRG(AIRy)=a (DAIR5 (y))
SDLEST(AIR,y)
Standard deviation of airborne
SDPEST(AIR,y)
delays occurring on O-D pairs
departing at airport a
delays occurring on O-D pairs
arriving at airport a
a ( DAIRY (y)
COEFFICIENTS OF VARIATION
CVaORG (TO
Y)
Coefficient of variation of taxi
out delays occurring on O-D
CVORG (TO, y) = SD.VRG(TOy)/
pairs originating at airport a
AVE( D
jTO)
(y))
y)
CVDEST
(TO Y)
Coefficient of variation of taxi
out delays occurring on O-D
pairs arriving at airport a
CVaDEST (TO,
CVORG
(TI, Y)
Coefficient of variation of taxi
in delays occurring on O-D
CVoRG (TI, y)
pairs originating at airport a
AVE(DTI
DTO" (y)
(
D
SDPEST(TO,y) /AVE(
SDORG(Tjy)
(y))
143
CVDEST (TI Y)
CV)RG
(AIR, y)
CVDEST (AIR, y)
Coefficient of variation of taxi
in delays occurring on O-D
pairs arriving at airport a
Coefficient of variation of
airborne delays occurring on 0D pairs originating at airport a
Coefficient of variation of
airborne delays occurring on 0D pairs arriving at airport a
CV aDEST (TI, y)= SDPEST(Tjy)
/
AVE( DTI" (y))
CV,,)RG
(AIR, y) =SDORG(AIR,y)/
AVE( DAIRg (y))
CVLEST (AIR, y)= SD2EST(AIR,y) /
AVE( DAIRaJ(y))
144
I
U
-
AIL
0.7
1.2
BWI
0.8
0.5
1.5
CLE
CLT
0.8
0.6
1.0
0.8
1.7
1.2
1.1
1.1
1.5
1.0
0.7
1.3
1.4
1.6
0.7
0.8
1.0
0.9
1.1
0.5
1.3
1.9
1.3
0.7
1.6
1.0
0.8
1.8
1.6
1.6
1.5
1.3
2.2
1.2
2.4
1.1
1.0
2.2
0.9
1.1
1.8
1.3
1.3
1.7
0.8
0.9
0.8
1.1
1.3
1.3
1.3
0.8
0.9
1.0
0.9
DTW
EWR
FLL
IAD
rAH
uAX
0
LGA
MCO
MEM
MIA
MSP
_
0.9
0.6
OR5
PHL
1.4
2.0
0.9
0.8
1.1
PHX_
PIT
0.8
0.9
1.7
_FO1.4
I FA
U.8
0.6
JALL
19
.|
STDEV Taxi Out Delay
-
U
'.h
0.7
C\/G
DCA
DEN
DFW
0
-
'1.Z
BO$
CM
I-
STDJEV Taxi Out Delay
1995
1997
2000
I
*i
I
-
ATL
BOS
BWI
G
DCA
I-
DFW
0
EWRT
z FLL
0 1
w
z
CO)
LGA
MCO
MIA
0.9
PHX
PIT
1.6
1.3
1.i
I FA
3U
!ALL
1995
1.b
2.1
2.0
2.0
1.7
2.1
1.8
2.2
1.8
1.5
1.6
1.7
1.9
2.8
1.5
2.1
1.8
1.9
1.5
1.4
1.5
1.7
1.7
2.3
1.7
2.0
1.3
1.
1.3
1.1
1.3
1.5
1.1
0.9
1.2
1.0
1.4
1.3
0.7
1.4
1.3
0.6
1.0
1.0
1.1
1.4
1.1
1.0
1.3
1.5
1.2
1.4
1.3
1.1
0.9
1.2
1.6
1.3
1.3
0.8
0.9
1.4
p-
1.5
1.3
1.2
z
MIA
1.3
1.2
1.5
MC_
PrE
1.1
1.3
1.3
0.8
1.1
1.0
MIA
1.2
1.4
1.5
1.0
1.1
_
__
CVG
C
0.9
o
1.0
W_0.7
EWR
0.9
w rE-1.1
S1.1
Z IA
PL
0.8
0.9
PHT
1.6
1.0
1.1
1.1
1.1
PIT
0.8
0.8
1.1
1.2
MSP
ORD
1- 1 - - .
2.3
1.9
2.5
2.1
2.5
1.8
2.5
2.4
2.2
.1
1.5
2.5
2.2
2.5
2.9
1.6
2.5
1.8
2.2
2.1
2.3
1.9
2.4
2.2
2.6
2000
2.9
2.9
2.9
3.3
3.2
3.7
2.8
2.8
3.2
3.2
.6
2.1
3.8
3.0
3.5
3.1
1.8
3.2
2.2
3.2
2.7
2.8
2.2
3.9
3.7
2.9
3.5
J.Ul
0.9
1.3
1.2
1.2
1.3
1.3
0.6
0.3
0.6
0.4
0.5
0.4
0.4
0.5
0.3
0.4
0.3
0.7
0.5
0.2
0.3
0.3
0.3
0.8
1.0
0.4
0.7
0.6
0.4
0.5
1.1
0.9
0.8
0.7
1.3
0.5
1.2
0.5
1.2
0.4
0.3
0.4
0.3
0.5
0.5
0.3
MIA
0.5
0.6
0.3
0.7
0.4
1.0
0.9
0.3
0.4
1.0
PHL
PFIX
0.6
0.7
0.3
0.4
0.6
0.6
0.7
0.7
0.6
0.5
0.7
1.0
PIT
0.3
0.4
0.3
0.3
0.4
0.6
0.
0.
____
EN
0 DFW-
0-
EWR
z
2000
0.5
CVG
o
19W/
.4
A1TL
BO
EW
.8
1.5
L
I
1.|2.21
1995
BOS
BWI
-~
STDEV Taxi In elay
5TDEV Taxi In Delay
0.7
-19V7
E0.3
I0.6
E0.7
C
O
1FA
.1~
0.8
1.1
0.4
0.4
0.7
145
AlL
ATL
BOS
BWI
C
CVG
DCA
0-
0
EWR
FLL
AD
L
0
M
_
_
_
_
MIA
R
PXPT
WA
1|
JALL
I
STDEV Airborne Delay
1u9v
1v
2uuu
2.6
3.7
2.6
3.7
4.1
3.9
4.1
4.1
2.8
4.9
4.7
3.2
2.7
3.5
3.1
2.8
4.5
3.1
3.4
3.0
2.6
4.2
3.0
2.9
2.2
1.7
2.6
2.5
1.6
2.1
3.1
4.4
3.2
3.7
3.9
3.0
4.3
2.0
3.3
4.5
3.4
2.9
5.4
1.9
2.3
3.4
3.4
4.2
4.0
3.8
3.5
2.5
2.5
3.0
3.8
3.3
1.5
3.1
3.1
2.5
3.4
3.1
2.7
3.1
2.8
2.5
2.9
4.8
4.1
4.2
2.6
3.9
3.0
5.1
3.3
3.4
4.0
4.0
3.3
2tl
~2.b
3.bj
J.41
STDEV Airborne Delay
I
ATL
BOS
C
CVG
I-
0
EWR
z
0
z
w
0l
MIA
O
PRE-PRX
I
3.2
3.b
__
0.14
_
CLE
CLT
CMH
CVG
DCA
DEN
DFW
0 _
CL
W FLL
R IAD
IAH
5 LX
I
0.10
0.14
0.15
0.15
0.26
0.22
0.18
0.13
0.15
0.17
0.13
0.18
0.16
0.15
0.12
0.22
0.18
0.16
0.20
0.19
0.20
0.25
0.17
0.12
0.14
0.17
0.24
0.121
0.16
0.15
0.15
LGA
0.12
0.12
0.15
MEM
0.29
0.24
0.13
0.14
0.22
0.23
0.18
0.21
0.21
0.26
0.17
0.10
0.22
0.19
0.17
0.22
MSP
ORD
PHL
PHX
P1'F
SFO
-
_
0.20
0.17
0.12
0.25
0.16
0.17
0.21
0.15
0.17
0.14
0.22
0.19
0.17
ITtW
0.
_OM3
.
-- 7 7 .T
0.19
0.23
0.13
0.14
0.13
0.13
0.23
0.17
O~
12.7|
.61
J.41
1.8
1.8
4.2
2.5
2.6
1.8
2.0
2.0
2.3
3.7
2.5
2.6
3.5
3.7
4.0
3.3
3.8
3.1
2.7
2.7
3.1
2.2
2.4
3.2
3.6
2.4
5.0
2.7
3.2
3.3
4.3
3.1
4.5
2.6
2.1
3.0
2.7
2.9
3.0
3.7
3.8
2.3
3.2
2.6
3.3
2.8
3.0
2.4
2.5
3.2
3.4
4.0
2.3
I VA
jALL
2.4
ir
--. m
COEFF VAR. Taxi Out Dela
COEFF VAR. Taxi Out Delay
B
2.109
2.0
2.1
2.9
4.3
2.6
3.7
1.6
1.4
2.9
3.7
2.5
2.2
2.8
1.9
3.0
4.0
1.9
3.0
2.4
3.5
2.4
1.9
2.3
4.6
3.6
3.2
B
0.35
CLE
CLT
MH
0.33
0.33
0.36
0.36
0.36
0.30
0.38
0.39
0.36
0.31
0.34
0.39
0.42
0.40
0.36
0.30
0.32
0.39
0.32
0.27
0.31
0.28
0.32
0.49
0.27
0.34
0.34
0.40
0.39
0.34
0.31
0.23
0.37
0.37
0.42
0.42
0.27
0.33
0.39
0.37
0.32
0.23
0.41
0.37
0.41
0.36
0.18
____
DCA
DEN
o
DFW
0.
o
FLL
IAD
~ IAH
U<
j- LGA
cl)
w N O
o MEM
MIA
MSP
_
ORD
PHL
PHX
SFO
,ALL
.
.
0.28
0.23
0.30
0.32
0.28
0.36
. 9
0.35
0.34
0.28
0.31
0.36
0.34
0.29
0.34
0.33
0.35
0.37
0.36
0.28
0.26
0.45
0.42
0.30
0.
-
~
O~
146
COEFF VAR. Taxi InDay
1997
1995
z0ou
-
0.35
BOS
BWI
CLE
CLT
CMH
CVG
DCA
DEN
0.49
U.ju
0.49
0.39
0.44
0.46
0.41
0.32
0.34
0.41
0.40
0.47
0.49
0.45
0.45
0.40
0.49
0.45
0.43
0.46
0.451
0.35
0.35
0.42
0.41
DFW
0.38
0.38
0.38
It0
I- DTW
0.36
0.40
0.32
0.33
0.48
0.40
0.
0.37
0.52
0.50
0.34
0.48
0.52
0.43
0.37
0.47
0.42
0.47
0.46
0.45
0.45
0.48
0.43
0.39
0.38
0.37
0.40
0.60
0.34
0.42
0.42
0.42
0.40
0.35
0.39
0.30
0.42
0.38
0.36
0.391
0
_WR
FLL
0.51
_AD
z IAH
0.55
LAX
0 LGA
M
MEM
MIA
ORD
PHL
PHX
p
SFO
U.3iL
__
I-
_
BWI
CLE
CLT
__
CVG
A
DEN
DFW
DTW
0 EWR
_LL
IAD
z IAH
LAX
0 LGA
M 0
MEM
MIA
Mw_
ORD
PHL
PHX
PIT
SFO
l~7-
JAL
_
U.iD
U.'-10
0.13
0.33
0.19
0.23
0.15
0.26
0.17
0.18
0.18
0.23
0.14
0.12
0.26
0.20
0.17
0.20
0.22
0.18
0.33
0.25
0.29
0.30
0.20
0.30
0.21
0.14
0.25
0.28
0.13
0.22
0.19
0.16
0.10
0.27
0.18
0.25
.2
0.25
0.15
0.22
0.17
0.12
0.25
0.27
0.20
0.34
0.17
0.18
0.24
0.25
0.14
0.23
0.27
0.30
0.22
0.26
0.17
0.32
0.22
0.7
0.19
0.21
0.17
0.18
0.19
0.31
0.14
01
PIT
SFO
0.1
0.16
0.2
0.19
0.1
0.24
TPA
JALL
U.24
U.1
U.441
u.;sv
__MH_
4c
CVG
D_A
DEN
DFW
DTW
EWR
FLL
AD
IAH
AX
LGA
w
|MC0
1-
z
p
0.38
0.42
0.39
0.31
0.43
a
MEM
MIA
______
PHL
ORD
PHX
MP0.17
ORD0.23
19971
0.39
0.36
0.36
0.46
0.50
0.47
0.33
0.37
0.39
0.481
0.34
0.36
0.42
.3
0.21
0.21
0.51
0.40
0.34
0.28
0.22
0.39
0.30
0.50
0.
0.28
0.30
0.45
0.40
CVG
bA
I- DEN
0 DFW
0.40
0.23
0.32
0.43
0.34
0.42
0.36
0.31
0.25
0.30
0.38
0.35
0.18
0.27
0.52
0.34
0.35
0.27
0.41
0.36
0.34
0
P
0.34
mw___
0.36
0.48
0.27
0.58
0.36
0.31
0.43
0.32
0.39
0.30
0.34
0.43
0.28
0.40
0.32
ORD
PHL
PHX
PIT
SFO
0.53
0.27
0.33
0.33
0.35
U. I7
-
0. 3
U.43
0.18
.3
0.1
0.28
0.19
0.35
0.34
0.29
0.23
0.30
0.25
0.29
0.33
0.31
0.25
0.31
0.31
0.28
0.31
0.29
0.33
0.50
0.47
0.35
0.63
0.31
0.35 0.30
0.25
0.37
0.26
0.37
0.48
0.22
0.27
0.34
0.30
0.33
0.25
0.25
0.32
0.39
0.50
0.23
0.33
0.29
0.22
0.29
0.35
0.32
0.49
0.19
0.35
0.34
0.19
0.24
0.31
0.32
0.34
0.31
D3
U7
0.26
0.41
0.59
0.38
0.61
a.
DTW
EWR
L
0.45
0.29
0.3
BWI
CLE
CLT
0.41
0.36
~
EF VAR. Airborne Dea
ea
Z0
OF VAR. Airorne
- 1995
~
BOS
BWI
CLE
CLT
0.40
0.46
U. -Ib
AT L
Al
I
COEFF VAR. Taxi in Delay
1997
1995
z0uu
U.'-16
F --.
p
cn
IAD
IAH
LAX
9A
0.27
M0.39
o MEM
MIA
L
0.26
ITW-
0.37
U.31
0.36
0.33
0.28
0.33
0.34
0.43
0.36
0.33
0.31
0.36
0.35
147